L. Levi, T. Schwartz, O. Manela, M. Segev, and H. Buljan, “Spontaneous pattern formation upon incoherent waves: From modulation-instability to steady-state,” Opt. Express 16, 7818–7831 (2008).

[CrossRef]
[PubMed]

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, “Incoherent spatial solitons in effectively instantaneous nonlinear media,” Nature Photon. 2, 371 (2008).

[CrossRef]

A. Picozzi, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett 101, 093901 (2008).

[CrossRef]
[PubMed]

H. Prakash and D. K. Singh, “Change in coherence properties and degree of polarization of light propagating in a lossless isotropic nonlinear Kerr medium,” J. Phys. B: At. Mol. Opt. Phys. 41, 045401 (2008).

[CrossRef]

S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express 16, 6646 (2008).

[CrossRef]
[PubMed]

S. Lagrange, H. R. Jauslin, and A. Picozzi, “Thermalization of the dispersive three-wave interaction,” Europhys. Lett. 79, 64001 (2007).

[CrossRef]

A. Picozzi, “Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics,” Opt. Express 15, 9063 (2007).

[CrossRef]
[PubMed]

W. Huang, S. A. Ponomarenko, M. Cada, and G. P. Agrawal, “Polarization changes of partially coherent pulses propagating in optical fibers,” J. Opt. Soc. Am. A 24, 3063 (2007).

[CrossRef]

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, “Random Generation of Coherent Solitary Waves from Incoherent Waves,” Phys. Rev. Lett. 96, 227202 (2006).

[CrossRef]
[PubMed]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).

[CrossRef]

A. Picozzi, “Nonequilibrated Oscillations of Coherence in Coupled Nonlinear Wave Systems,” Phys. Rev. Lett. 96, 013905 (2006).

[CrossRef]
[PubMed]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902 (2006).

[CrossRef]
[PubMed]

A. Sauter, S. Pitois, G. Millot, and A. Picozzi, “Incoherent modulation instability in instantaneous nonlinear Kerr media,” Opt. Lett. 30, 2143–2145 (2005).

[CrossRef]
[PubMed]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005).

[CrossRef]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88 (2005).

[CrossRef]

V. E. Zakharov and S. V. Nazarenko, “Dynamics of the Bose-Einstein condensation,” Physica D 201, 203–211 (2005).

[CrossRef]

A. Picozzi and P. Aschieri, “Influence of dispersion on the resonant interaction between three incoherent waves,” Phys. Rev. E 72, 046606 (2005).

[CrossRef]

A. Schauer, I. V. Melnikov, and J. S. Aitchison, “Collisions of orthogonally polarized spatial solitons in AlGaAs slab waveguides,” J. Opt. Soc. Am. B 21, 57 (2004).

[CrossRef]

A. Picozzi, “Entropy and degree of polarization for nonlinear optical waves,” Opt. Lett. 29, 1653 (2004).

[CrossRef]
[PubMed]

V. E. Zakharov, F. Dias, and A. Pushkarev, “One-dimensional wave turbulence,” Phys. Rep. 398, 1 (2004).

[CrossRef]

A. Picozzi and M. Haelterman, “Condensation in Hamiltonian Parametric Wave Interaction,” Phys. Rev. Lett. 92, 103901 (2004).

[CrossRef]
[PubMed]

S. A. Ponomarenko and G. P. Agrawal, “Asymmetric incoherent vector solitons,” Phys. Rev. E 69, 036604 (2004).

[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett. 92, 143906 (2004).

[CrossRef]
[PubMed]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).

[CrossRef]

A. Picozzi, C. Montes, and M. Haelterman, “Coherence properties of the parametric three-wave interaction driven from an incoherent pump,” Phys. Rev. E 66, 056605 (2002).

[CrossRef]

B. Rumpf and A. C. Newell, “Coherent Structures and Entropy in Constrained, Modulationally Unstable Nonintegrable Systems,” Phys. Rev. Lett. 87, 054102 (2001).

[CrossRef]
[PubMed]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601 (2001).

[CrossRef]

A. Picozzi and M. Haelterman, “Parametric Three-Wave Soliton Generated from Incoherent Light,” Phys. Rev. Lett. 86, 2010–2013 (2001).

[CrossRef]
[PubMed]

A. C. Newell, S. Nazarenko, and L. Biven, “Wave turbulence and intermittency,” Physica D 152, 520 (2001).

[CrossRef]

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[CrossRef]

G. P. Agrawal and E. Wolf, “Propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A 17, 2019 (2000).

[CrossRef]

R. Jordan and C. Josserand, “Self-organization in nonlinear wave turbulence,” Phys. Rev. E 61, 1527–1539 (2000).

[CrossRef]

P. Ohberg and S. Stenholm, “Internal Josephson effect in trapped double condensates,” Phys. Rev. A 59, 3890 (1999).

[CrossRef]

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (John Wiley & Sons, 1998).

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880 (1997).

[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of Incoherent Self-Focusing in Biased Photorefractive Media,” Phys. Rev. Lett. 78, 646 (1997).

[CrossRef]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990 (1997).

[CrossRef]

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[CrossRef]

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[CrossRef]

M. Mitchell, Z. Chen, Ming-feng Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490 (1996).

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[CrossRef]

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[CrossRef]
[PubMed]

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[CrossRef]

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[CrossRef]

W. Huang, S. A. Ponomarenko, M. Cada, and G. P. Agrawal, “Polarization changes of partially coherent pulses propagating in optical fibers,” J. Opt. Soc. Am. A 24, 3063 (2007).

[CrossRef]

S. A. Ponomarenko and G. P. Agrawal, “Asymmetric incoherent vector solitons,” Phys. Rev. E 69, 036604 (2004).

[CrossRef]

G. P. Agrawal and E. Wolf, “Propagation-induced polarization changes in partially coherent optical beams,” J. Opt. Soc. Am. A 17, 2019 (2000).

[CrossRef]

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A. Schauer, I. V. Melnikov, and J. S. Aitchison, “Collisions of orthogonally polarized spatial solitons in AlGaAs slab waveguides,” J. Opt. Soc. Am. B 21, 57 (2004).

[CrossRef]

D.C. Hutchings, J. S. Aitchison, and J. M. Arnold, “Nonlinear refractive coupling and vector solitons in anisotropic cubic media,” J. Opt. Soc. Am. B 14, 869 (1997).

[CrossRef]

J. U. Kangand, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov Spatial Solitons in AlGaAs Planar Waveguides,” Phys. Rev. Lett 76, 3699 (1996).

[CrossRef]

J. U. Kangand, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov Spatial Solitons in AlGaAs Planar Waveguides,” Phys. Rev. Lett 76, 3699 (1996).

[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).

[CrossRef]

A. Picozzi and P. Aschieri, “Influence of dispersion on the resonant interaction between three incoherent waves,” Phys. Rev. E 72, 046606 (2005).

[CrossRef]

B. Barviau, B. Kibler, S. Coen, and A. Picozzi, “Towards a thermodynamic description of supercontinuum generation,” Opt. Lett. (to be published).

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[CrossRef]

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[CrossRef]

A. C. Newell, S. Nazarenko, and L. Biven, “Wave turbulence and intermittency,” Physica D 152, 520 (2001).

[CrossRef]

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (John Wiley & Sons, 1998).

L. Levi, T. Schwartz, O. Manela, M. Segev, and H. Buljan, “Spontaneous pattern formation upon incoherent waves: From modulation-instability to steady-state,” Opt. Express 16, 7818–7831 (2008).

[CrossRef]
[PubMed]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).

[CrossRef]

M. Mitchell, Z. Chen, Ming-feng Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490 (1996).

[CrossRef]
[PubMed]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601 (2001).

[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of Incoherent Self-Focusing in Biased Photorefractive Media,” Phys. Rev. Lett. 78, 646 (1997).

[CrossRef]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990 (1997).

[CrossRef]

M. Segev and D. N. Christodoulides, Incoherent Solitons, Eds. S. Trillo and W. Torruellas, Spatial Solitons (Springer, Berlin, 2001).

B. Barviau, B. Kibler, S. Coen, and A. Picozzi, “Towards a thermodynamic description of supercontinuum generation,” Opt. Lett. (to be published).

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, “Incoherent spatial solitons in effectively instantaneous nonlinear media,” Nature Photon. 2, 371 (2008).

[CrossRef]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).

[CrossRef]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005).

[CrossRef]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990 (1997).

[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601 (2001).

[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of Incoherent Self-Focusing in Biased Photorefractive Media,” Phys. Rev. Lett. 78, 646 (1997).

[CrossRef]

C. M. de Sterke and J. E. Sipe, “Polarization instability in a waveguide geometry,” Opt. Lett 16, 202 (1991).

[CrossRef]
[PubMed]

V. E. Zakharov, F. Dias, and A. Pushkarev, “One-dimensional wave turbulence,” Phys. Rep. 398, 1 (2004).

[CrossRef]

G. During, A. Picozzi, and S. Rica, “Breakdown of wave turbulence and nonlinear wave condensation,” Physica D (to be published).

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation,” Physica D 57, 96 (1992).

[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601 (2001).

[CrossRef]

V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, Berlin, 1992).

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).

[CrossRef]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).

[CrossRef]

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S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88 (2005).

[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett. 92, 143906 (2004).

[CrossRef]
[PubMed]

A. Picozzi and M. Haelterman, “Condensation in Hamiltonian Parametric Wave Interaction,” Phys. Rev. Lett. 92, 103901 (2004).

[CrossRef]
[PubMed]

A. Picozzi, C. Montes, and M. Haelterman, “Coherence properties of the parametric three-wave interaction driven from an incoherent pump,” Phys. Rev. E 66, 056605 (2002).

[CrossRef]

A. Picozzi and M. Haelterman, “Parametric Three-Wave Soliton Generated from Incoherent Light,” Phys. Rev. Lett. 86, 2010–2013 (2001).

[CrossRef]
[PubMed]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).

[CrossRef]

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[CrossRef]

S. Lagrange, H. R. Jauslin, and A. Picozzi, “Thermalization of the dispersive three-wave interaction,” Europhys. Lett. 79, 64001 (2007).

[CrossRef]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902 (2006).

[CrossRef]
[PubMed]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88 (2005).

[CrossRef]

R. Jordan and C. Josserand, “Self-organization in nonlinear wave turbulence,” Phys. Rev. E 61, 1527–1539 (2000).

[CrossRef]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005).

[CrossRef]

R. Jordan and C. Josserand, “Self-organization in nonlinear wave turbulence,” Phys. Rev. E 61, 1527–1539 (2000).

[CrossRef]

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, “Random Generation of Coherent Solitary Waves from Incoherent Waves,” Phys. Rev. Lett. 96, 227202 (2006).

[CrossRef]
[PubMed]

J. U. Kangand, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov Spatial Solitons in AlGaAs Planar Waveguides,” Phys. Rev. Lett 76, 3699 (1996).

[CrossRef]

B. Barviau, B. Kibler, S. Coen, and A. Picozzi, “Towards a thermodynamic description of supercontinuum generation,” Opt. Lett. (to be published).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons : From Fibers to Photonic Crystals (Ac. Press, 2003).

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, “Random Generation of Coherent Solitary Waves from Incoherent Waves,” Phys. Rev. Lett. 96, 227202 (2006).

[CrossRef]
[PubMed]

V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, Berlin, 1992).

S. Lagrange, H. R. Jauslin, and A. Picozzi, “Thermalization of the dispersive three-wave interaction,” Europhys. Lett. 79, 64001 (2007).

[CrossRef]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902 (2006).

[CrossRef]
[PubMed]

M. Le Bellac, F. Mortessagne, and G. Batrouni, Equilibrium and Nonequilibrium Statistical Thermodynamics (Cambridge Univ. Press, 2004).

[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).

[CrossRef]

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S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express 16, 6646 (2008).

[CrossRef]
[PubMed]

A. Picozzi, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett 101, 093901 (2008).

[CrossRef]
[PubMed]

A. Sauter, S. Pitois, G. Millot, and A. Picozzi, “Incoherent modulation instability in instantaneous nonlinear Kerr media,” Opt. Lett. 30, 2143–2145 (2005).

[CrossRef]
[PubMed]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88 (2005).

[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett. 92, 143906 (2004).

[CrossRef]
[PubMed]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601 (2001).

[CrossRef]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880 (1997).

[CrossRef]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990 (1997).

[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of Incoherent Self-Focusing in Biased Photorefractive Media,” Phys. Rev. Lett. 78, 646 (1997).

[CrossRef]

M. Mitchell, Z. Chen, Ming-feng Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490 (1996).

[CrossRef]
[PubMed]

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A. Picozzi, C. Montes, and M. Haelterman, “Coherence properties of the parametric three-wave interaction driven from an incoherent pump,” Phys. Rev. E 66, 056605 (2002).

[CrossRef]

M. Le Bellac, F. Mortessagne, and G. Batrouni, Equilibrium and Nonequilibrium Statistical Thermodynamics (Cambridge Univ. Press, 2004).

[CrossRef]

A. C. Newell, S. Nazarenko, and L. Biven, “Wave turbulence and intermittency,” Physica D 152, 520 (2001).

[CrossRef]

V. E. Zakharov and S. V. Nazarenko, “Dynamics of the Bose-Einstein condensation,” Physica D 201, 203–211 (2005).

[CrossRef]

B. Rumpf and A. C. Newell, “Coherent Structures and Entropy in Constrained, Modulationally Unstable Nonintegrable Systems,” Phys. Rev. Lett. 87, 054102 (2001).

[CrossRef]
[PubMed]

A. C. Newell, S. Nazarenko, and L. Biven, “Wave turbulence and intermittency,” Physica D 152, 520 (2001).

[CrossRef]

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation,” Physica D 57, 96 (1992).

[CrossRef]

A. C. Newell, “The closure problem in a system of random gravity waves,” Rev. of Geophys. 6, 1–31 (1968).

[CrossRef]

A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley Publ. Comp., 1992).

E. L. O’Neill, Introduction to Statistical Optics (Dover Publ., New York, 1963).

P. Ohberg and S. Stenholm, “Internal Josephson effect in trapped double condensates,” Phys. Rev. A 59, 3890 (1999).

[CrossRef]

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, “Random Generation of Coherent Solitary Waves from Incoherent Waves,” Phys. Rev. Lett. 96, 227202 (2006).

[CrossRef]
[PubMed]

A. Picozzi, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett 101, 093901 (2008).

[CrossRef]
[PubMed]

S. Lagrange, H. R. Jauslin, and A. Picozzi, “Thermalization of the dispersive three-wave interaction,” Europhys. Lett. 79, 64001 (2007).

[CrossRef]

A. Picozzi, “Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics,” Opt. Express 15, 9063 (2007).

[CrossRef]
[PubMed]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902 (2006).

[CrossRef]
[PubMed]

A. Picozzi, “Nonequilibrated Oscillations of Coherence in Coupled Nonlinear Wave Systems,” Phys. Rev. Lett. 96, 013905 (2006).

[CrossRef]
[PubMed]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005).

[CrossRef]

A. Sauter, S. Pitois, G. Millot, and A. Picozzi, “Incoherent modulation instability in instantaneous nonlinear Kerr media,” Opt. Lett. 30, 2143–2145 (2005).

[CrossRef]
[PubMed]

A. Picozzi and P. Aschieri, “Influence of dispersion on the resonant interaction between three incoherent waves,” Phys. Rev. E 72, 046606 (2005).

[CrossRef]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88 (2005).

[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett. 92, 143906 (2004).

[CrossRef]
[PubMed]

A. Picozzi and M. Haelterman, “Condensation in Hamiltonian Parametric Wave Interaction,” Phys. Rev. Lett. 92, 103901 (2004).

[CrossRef]
[PubMed]

A. Picozzi, “Entropy and degree of polarization for nonlinear optical waves,” Opt. Lett. 29, 1653 (2004).

[CrossRef]
[PubMed]

A. Picozzi, C. Montes, and M. Haelterman, “Coherence properties of the parametric three-wave interaction driven from an incoherent pump,” Phys. Rev. E 66, 056605 (2002).

[CrossRef]

A. Picozzi and M. Haelterman, “Parametric Three-Wave Soliton Generated from Incoherent Light,” Phys. Rev. Lett. 86, 2010–2013 (2001).

[CrossRef]
[PubMed]

G. During, A. Picozzi, and S. Rica, “Breakdown of wave turbulence and nonlinear wave condensation,” Physica D (to be published).

B. Barviau, B. Kibler, S. Coen, and A. Picozzi, “Towards a thermodynamic description of supercontinuum generation,” Opt. Lett. (to be published).

A. Picozzi and S. Rica, “Coherence absorption induced by thermalization of incoherent fields” Europhys. Lett. (to be published).

A. Picozzi, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett 101, 093901 (2008).

[CrossRef]
[PubMed]

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[CrossRef]
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[CrossRef]
[PubMed]

A. Sauter, S. Pitois, G. Millot, and A. Picozzi, “Incoherent modulation instability in instantaneous nonlinear Kerr media,” Opt. Lett. 30, 2143–2145 (2005).

[CrossRef]
[PubMed]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88 (2005).

[CrossRef]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett. 92, 143906 (2004).

[CrossRef]
[PubMed]

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[CrossRef]

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[CrossRef]

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[CrossRef]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005).

[CrossRef]

A. Picozzi and S. Rica, “Coherence absorption induced by thermalization of incoherent fields” Europhys. Lett. (to be published).

G. During, A. Picozzi, and S. Rica, “Breakdown of wave turbulence and nonlinear wave condensation,” Physica D (to be published).

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[CrossRef]

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[CrossRef]
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[CrossRef]

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[CrossRef]
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C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, “Incoherent spatial solitons in effectively instantaneous nonlinear media,” Nature Photon. 2, 371 (2008).

[CrossRef]

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[CrossRef]

L. Levi, T. Schwartz, O. Manela, M. Segev, and H. Buljan, “Spontaneous pattern formation upon incoherent waves: From modulation-instability to steady-state,” Opt. Express 16, 7818–7831 (2008).

[CrossRef]
[PubMed]

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, “Incoherent spatial solitons in effectively instantaneous nonlinear media,” Nature Photon. 2, 371 (2008).

[CrossRef]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).

[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601 (2001).

[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of Incoherent Self-Focusing in Biased Photorefractive Media,” Phys. Rev. Lett. 78, 646 (1997).

[CrossRef]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990 (1997).

[CrossRef]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880 (1997).

[CrossRef]

M. Mitchell, Z. Chen, Ming-feng Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490 (1996).

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M. Mitchell, Z. Chen, Ming-feng Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490 (1996).

[CrossRef]
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H. Prakash and D. K. Singh, “Change in coherence properties and degree of polarization of light propagating in a lossless isotropic nonlinear Kerr medium,” J. Phys. B: At. Mol. Opt. Phys. 41, 045401 (2008).

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J. U. Kangand, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov Spatial Solitons in AlGaAs Planar Waveguides,” Phys. Rev. Lett 76, 3699 (1996).

[CrossRef]

P. Ohberg and S. Stenholm, “Internal Josephson effect in trapped double condensates,” Phys. Rev. A 59, 3890 (1999).

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M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, “Random Generation of Coherent Solitary Waves from Incoherent Waves,” Phys. Rev. Lett. 96, 227202 (2006).

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V. E. Zakharov, F. Dias, and A. Pushkarev, “One-dimensional wave turbulence,” Phys. Rep. 398, 1 (2004).

[CrossRef]

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation,” Physica D 57, 96 (1992).

[CrossRef]

V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, Berlin, 1992).

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S. Lagrange, H. R. Jauslin, and A. Picozzi, “Thermalization of the dispersive three-wave interaction,” Europhys. Lett. 79, 64001 (2007).

[CrossRef]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88 (2005).

[CrossRef]

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[CrossRef]

H. Prakash and D. K. Singh, “Change in coherence properties and degree of polarization of light propagating in a lossless isotropic nonlinear Kerr medium,” J. Phys. B: At. Mol. Opt. Phys. 41, 045401 (2008).

[CrossRef]

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature (London) 387, 880 (1997).

[CrossRef]

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, “Incoherent spatial solitons in effectively instantaneous nonlinear media,” Nature Photon. 2, 371 (2008).

[CrossRef]

L. Levi, T. Schwartz, O. Manela, M. Segev, and H. Buljan, “Spontaneous pattern formation upon incoherent waves: From modulation-instability to steady-state,” Opt. Express 16, 7818–7831 (2008).

[CrossRef]
[PubMed]

A. Picozzi, “Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics,” Opt. Express 15, 9063 (2007).

[CrossRef]
[PubMed]

S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express 16, 6646 (2008).

[CrossRef]
[PubMed]

C. M. de Sterke and J. E. Sipe, “Polarization instability in a waveguide geometry,” Opt. Lett 16, 202 (1991).

[CrossRef]
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J. E. Heebner, R. Bennink, R. W. Boyd, and R. Fisher, “Conversion of unpolarized light to polarized light with greater than 50% efficiency by photorefractive two-beam coupling,” Opt. Lett. 25, 257 (2000).

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A. Picozzi, “Entropy and degree of polarization for nonlinear optical waves,” Opt. Lett. 29, 1653 (2004).

[CrossRef]
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A. Sauter, S. Pitois, G. Millot, and A. Picozzi, “Incoherent modulation instability in instantaneous nonlinear Kerr media,” Opt. Lett. 30, 2143–2145 (2005).

[CrossRef]
[PubMed]

V. E. Zakharov, F. Dias, and A. Pushkarev, “One-dimensional wave turbulence,” Phys. Rep. 398, 1 (2004).

[CrossRef]

P. Ohberg and S. Stenholm, “Internal Josephson effect in trapped double condensates,” Phys. Rev. A 59, 3890 (1999).

[CrossRef]

Yu. P. Svirko and N. I. Zheludev, “Propagation of partially polarized light,” Phys. Rev. A 50, 709 (1994).

[CrossRef]
[PubMed]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).

[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, “Equivalence of three approaches describing partially incoherent wave propagation in inertial nonlinear media,” Phys. Rev. E 63, 035601 (2001).

[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, “Statistical theory for incoherent light propagation in nonlinear media,” Phys. Rev. E 65, 035602 (2002).

[CrossRef]

S. A. Ponomarenko and G. P. Agrawal, “Asymmetric incoherent vector solitons,” Phys. Rev. E 69, 036604 (2004).

[CrossRef]

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[CrossRef]

A. Picozzi, C. Montes, and M. Haelterman, “Coherence properties of the parametric three-wave interaction driven from an incoherent pump,” Phys. Rev. E 66, 056605 (2002).

[CrossRef]

A. Picozzi and P. Aschieri, “Influence of dispersion on the resonant interaction between three incoherent waves,” Phys. Rev. E 72, 046606 (2005).

[CrossRef]

J. U. Kangand, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov Spatial Solitons in AlGaAs Planar Waveguides,” Phys. Rev. Lett 76, 3699 (1996).

[CrossRef]

A. Picozzi, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett 101, 093901 (2008).

[CrossRef]
[PubMed]

A. Picozzi and M. Haelterman, “Condensation in Hamiltonian Parametric Wave Interaction,” Phys. Rev. Lett. 92, 103901 (2004).

[CrossRef]
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A. Picozzi, “Nonequilibrated Oscillations of Coherence in Coupled Nonlinear Wave Systems,” Phys. Rev. Lett. 96, 013905 (2006).

[CrossRef]
[PubMed]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of Classical Nonlinear Waves,” Phys. Rev. Lett. 95, 263901 (2005).

[CrossRef]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, “Velocity Locking of Incoherent Nonlinear Wave Packets,” Phys. Rev. Lett. 97, 033902 (2006).

[CrossRef]
[PubMed]

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, “Random Generation of Coherent Solitary Waves from Incoherent Waves,” Phys. Rev. Lett. 96, 227202 (2006).

[CrossRef]
[PubMed]

A. Picozzi and M. Haelterman, “Parametric Three-Wave Soliton Generated from Incoherent Light,” Phys. Rev. Lett. 86, 2010–2013 (2001).

[CrossRef]
[PubMed]

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Spectral incoherent solitons: a localized soliton behavior in the frequency domain,” Phys. Rev. Lett. 92, 143906 (2004).

[CrossRef]
[PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Theory of Incoherent Self-Focusing in Biased Photorefractive Media,” Phys. Rev. Lett. 78, 646 (1997).

[CrossRef]

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79, 4990 (1997).

[CrossRef]

M. Mitchell, Z. Chen, Ming-feng Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77, 490 (1996).

[CrossRef]
[PubMed]

B. Rumpf and A. C. Newell, “Coherent Structures and Entropy in Constrained, Modulationally Unstable Nonintegrable Systems,” Phys. Rev. Lett. 87, 054102 (2001).

[CrossRef]
[PubMed]

V. E. Zakharov and S. V. Nazarenko, “Dynamics of the Bose-Einstein condensation,” Physica D 201, 203–211 (2005).

[CrossRef]

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, “Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation,” Physica D 57, 96 (1992).

[CrossRef]

A. C. Newell, S. Nazarenko, and L. Biven, “Wave turbulence and intermittency,” Physica D 152, 520 (2001).

[CrossRef]

D. J. Benney and P. G. Saffman, “Nonlinear interactions of random waves in a dispersive medium,” Proc. R. Soc. London Ser. A289, 301 (1966).

[CrossRef]

A. C. Newell, “The closure problem in a system of random gravity waves,” Rev. of Geophys. 6, 1–31 (1968).

[CrossRef]

V. N. Tsytovich, Nonlinear Effects in Plasma (Plenum N.Y., 1970).

A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, 1975).

[CrossRef]

R. Z. Sagdeev, D. A. Usikov, and G. M. Zaslavsky, Nonlinear Physics (Harwood Publ., 1988).

V. E. Zakharov, V. S. L’vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer, Berlin, 1992).

M. Le Bellac, F. Mortessagne, and G. Batrouni, Equilibrium and Nonequilibrium Statistical Thermodynamics (Cambridge Univ. Press, 2004).

[CrossRef]

The elements Jij(z) do not depend on the spatial position r because of the assumption of homogeneous statistics [5, 10, 11]. Note also that the degree of polarization do not depend on the basis of polarization in which it is calculated [9].

Note that the property 〈|E+|2〉(z)=〈|E-|2〉(z) has not been observed for an intensity of the field grater than the critical intensity of polarization instability, 𝓘 > 𝓘c.

Conversely, in the case of incoherently coupled NLS equations, one has to introduce two distinct Lagrange’s multipliers µx and µy for each conserved quantity 𝓘x and 𝓘y, as discussed in details in Ref.[31].

M. Segev and D. N. Christodoulides, Incoherent Solitons, Eds. S. Trillo and W. Torruellas, Spatial Solitons (Springer, Berlin, 2001).

R. W. Boyd, Nonlinear Optics (Acad. Press, Third Ed., 2008).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons : From Fibers to Photonic Crystals (Ac. Press, 2003).

G. P. Agrawal, Nonlinear Fiber Optics (Acad. Press., New York, 2001).

A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley Publ. Comp., 1992).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).

J. W. Goodman, Statistical Optics (Wiley-Interscience Publ., New York, 1985).

E. L. O’Neill, Introduction to Statistical Optics (Dover Publ., New York, 1963).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge Univ. Press, 2007).

C. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (John Wiley & Sons, 1998).

Yu. P. Svirko and N. I. Zheludev, Polarization of Light in Nonlinear Optics (Wiley & Sons, 2000).

G. During, A. Picozzi, and S. Rica, “Breakdown of wave turbulence and nonlinear wave condensation,” Physica D (to be published).

B. Barviau, B. Kibler, S. Coen, and A. Picozzi, “Towards a thermodynamic description of supercontinuum generation,” Opt. Lett. (to be published).

A. Picozzi and S. Rica, “Coherence absorption induced by thermalization of incoherent fields” Europhys. Lett. (to be published).