J. Garnier, G. Xu, S. Trillo, and A. Picozzi, “Incoherent dispersive shocks in the spectral evolution of random waves,” Phys. Rev. Lett. 111, 113902 (2013).

[CrossRef]

K. Nithyanandan and K. Porsezian, “Interplay between relaxation of nonlinear response and coupling coefficient dispersion in the instability spectra of dual core optical fiber,” Opt. Commun. 303, 46–55 (2013).

[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, “Emergence of spectral incoherent solitons through supercontinuum generation in photonic crystal fiber,” Phys. Rev. E 84, 066605 (2011).

[CrossRef]

C. Condit, M. A. Schmidt, P. St, J. Russel, and F. Biancalana, “Highly noninstantaneous solitons in liquid-core photonic crystal fibers,” Phys. Rev. Lett. 105, 263902 (2010).

[CrossRef]

A. A. Canabarro, B. Santos, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Interplay of XPM and nonlinear response time in the modulational instability of copropagating optical pulses,” J. Opt. Soc. Am. B 27, 1878–1885 (2010).

[CrossRef]

M. Stepić, A. Maluckov, M. Stojanović, F. Chen, and D. Kip, “Modulational instability and solitary waves in one-dimensional lattices with intensity-resonant nonlinearity,” Phys. Rev. A 78, 043819 (2008).

[CrossRef]

T. Hansson, D. Anderson, M. Lisak, V. E. Semenov, and U. Österberg, “Quasilinear evolution and saturation of the modulational instability of partially coherent optical waves,” Phys. Rev. A 78, 011807 (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]

X. Liu, J. W. Haus, and S. M. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008).

[CrossRef]

M. Centurion, M. A. Porter, Y. Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and D. Psaltis, “Modulational instability in nonlinearity-managed optical media,” Phys. Rev. A 75, 063804 (2007).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

M. Onorato, A. R. Osborne, and M. Serio, “Modulation instability in crossing sea states: a possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96, 014503 (2006).

[CrossRef]

J. Fatome, S. Pitois, and G. Millot, “Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability,” Opt. Fiber Technol. 12, 243–250 (2006).

[CrossRef]

L. D. Carr and J. Brand, “Spontaneous soliton formation and modulational instability in Bose–Einstein condensates,” Phys. Rev. Lett. 92, 040401 (2004).

[CrossRef]

I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).

[CrossRef]

Y. D. Gong, P. Shum, D. Tang, C. Lu, and X. Guo, “660 GHz solitons source based on modulation instability in short cavity,” Opt. Express 11, 2480–2485 (2003).

[CrossRef]

C. Cambournac, H. Maillotte, E. Lantz, J. M. Dudley, and M. Chauvet, “Spatiotemporal behavior of periodic arrays of spatial solitons in a planar waveguide with relaxing Kerr nonlinearity,” J. Opt. Soc. Am. B 19, 574–585 (2002).

[CrossRef]

V. V. Konotop and M. Salerno, “Modulational instability in Bose–Einstein condensates in optical lattices,” Phys. Rev. A 65, 021602 (2002).

[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]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]

D. Kip, M. Soljacić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]

S. B. Cavalcanti, M. Yu, and G. P. Agrawal, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).

[CrossRef]

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).

[CrossRef]

S. B. Cavalcanti, M. Yu, and G. P. Agrawal, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).

[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

T. Hansson, D. Anderson, M. Lisak, V. E. Semenov, and U. Österberg, “Quasilinear evolution and saturation of the modulational instability of partially coherent optical waves,” Phys. Rev. A 78, 011807 (2008).

[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]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, “Emergence of spectral incoherent solitons through supercontinuum generation in photonic crystal fiber,” Phys. Rev. E 84, 066605 (2011).

[CrossRef]

C. Condit, M. A. Schmidt, P. St, J. Russel, and F. Biancalana, “Highly noninstantaneous solitons in liquid-core photonic crystal fibers,” Phys. Rev. Lett. 105, 263902 (2010).

[CrossRef]

L. D. Carr and J. Brand, “Spontaneous soliton formation and modulational instability in Bose–Einstein condensates,” Phys. Rev. Lett. 92, 040401 (2004).

[CrossRef]

G. Carbou and B. Hanouzet, “Relaxation approximation of the Kerr model for the impedance initial-boundary value problem,” in Proceedings of the 6th AIMS International Conference (2007), paper 212220.

L. D. Carr and J. Brand, “Spontaneous soliton formation and modulational instability in Bose–Einstein condensates,” Phys. Rev. Lett. 92, 040401 (2004).

[CrossRef]

S. B. Cavalcanti, M. Yu, and G. P. Agrawal, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).

[CrossRef]

M. Centurion, M. A. Porter, Y. Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and D. Psaltis, “Modulational instability in nonlinearity-managed optical media,” Phys. Rev. A 75, 063804 (2007).

[CrossRef]

M. Stepić, A. Maluckov, M. Stojanović, F. Chen, and D. Kip, “Modulational instability and solitary waves in one-dimensional lattices with intensity-resonant nonlinearity,” Phys. Rev. A 78, 043819 (2008).

[CrossRef]

J. Klinger, H. Martin, and Z. Chen, “Experiments on induced modulational instability of an incoherent optical beam,” Opt. Lett. 26, 271–273 (2001).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]

C.-S. Chou and M.-F. Shih, “Slow light achieved by non-instantaneous modulation instability,” J. Opt. A Pure Appl. Opt. 11, 105204 (2009).

[CrossRef]

D. Kip, M. Soljacić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).

[CrossRef]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., doi:10.1016/2014.03.002 (to be published).

[CrossRef]

C. Condit, M. A. Schmidt, P. St, J. Russel, and F. Biancalana, “Highly noninstantaneous solitons in liquid-core photonic crystal fibers,” Phys. Rev. Lett. 105, 263902 (2010).

[CrossRef]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).

[CrossRef]

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).

[CrossRef]

D. Kip, M. Soljacić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).

[CrossRef]

J. Fatome, S. Pitois, and G. Millot, “Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability,” Opt. Fiber Technol. 12, 243–250 (2006).

[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]

M. Centurion, M. A. Porter, Y. Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and D. Psaltis, “Modulational instability in nonlinearity-managed optical media,” Phys. Rev. A 75, 063804 (2007).

[CrossRef]

J. Garnier, G. Xu, S. Trillo, and A. Picozzi, “Incoherent dispersive shocks in the spectral evolution of random waves,” Phys. Rev. Lett. 111, 113902 (2013).

[CrossRef]

B. Kliber, C. Michel, J. Garnier, and A. Picozzi, “Temporal dynamics of incoherent waves in noninstantaneous response nonlinear Kerr media,” Opt. Lett. 37, 2472–2474 (2012).

[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., doi:10.1016/2014.03.002 (to be published).

[CrossRef]

A. A. Canabarro, B. Santos, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Interplay of XPM and nonlinear response time in the modulational instability of copropagating optical pulses,” J. Opt. Soc. Am. B 27, 1878–1885 (2010).

[CrossRef]

G. L. da Silva, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Modulational instability in lossless fibers with saturable delayed nonlinear response,” J. Opt. Soc. Am. B 26, 183–188 (2009).

[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]

G. Carbou and B. Hanouzet, “Relaxation approximation of the Kerr model for the impedance initial-boundary value problem,” in Proceedings of the 6th AIMS International Conference (2007), paper 212220.

T. Hansson, D. Anderson, M. Lisak, V. E. Semenov, and U. Österberg, “Quasilinear evolution and saturation of the modulational instability of partially coherent optical waves,” Phys. Rev. A 78, 011807 (2008).

[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., doi:10.1016/2014.03.002 (to be published).

[CrossRef]

X. Liu, J. W. Haus, and S. M. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

M. Centurion, M. A. Porter, Y. Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and D. Psaltis, “Modulational instability in nonlinearity-managed optical media,” Phys. Rev. A 75, 063804 (2007).

[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, “Emergence of spectral incoherent solitons through supercontinuum generation in photonic crystal fiber,” Phys. Rev. E 84, 066605 (2011).

[CrossRef]

M. Stepić, A. Maluckov, M. Stojanović, F. Chen, and D. Kip, “Modulational instability and solitary waves in one-dimensional lattices with intensity-resonant nonlinearity,” Phys. Rev. A 78, 043819 (2008).

[CrossRef]

D. Kip, M. Soljacić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).

[CrossRef]

V. V. Konotop and M. Salerno, “Modulational instability in Bose–Einstein condensates in optical lattices,” Phys. Rev. A 65, 021602 (2002).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, “Emergence of spectral incoherent solitons through supercontinuum generation in photonic crystal fiber,” Phys. Rev. E 84, 066605 (2011).

[CrossRef]

T. Hansson, D. Anderson, M. Lisak, V. E. Semenov, and U. Österberg, “Quasilinear evolution and saturation of the modulational instability of partially coherent optical waves,” Phys. Rev. A 78, 011807 (2008).

[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]

X. Liu, J. W. Haus, and S. M. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008).

[CrossRef]

A. A. Canabarro, B. Santos, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Interplay of XPM and nonlinear response time in the modulational instability of copropagating optical pulses,” J. Opt. Soc. Am. B 27, 1878–1885 (2010).

[CrossRef]

G. L. da Silva, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Modulational instability in lossless fibers with saturable delayed nonlinear response,” J. Opt. Soc. Am. B 26, 183–188 (2009).

[CrossRef]

M. Stepić, A. Maluckov, M. Stojanović, F. Chen, and D. Kip, “Modulational instability and solitary waves in one-dimensional lattices with intensity-resonant nonlinearity,” Phys. Rev. A 78, 043819 (2008).

[CrossRef]

B. Kliber, C. Michel, J. Garnier, and A. Picozzi, “Temporal dynamics of incoherent waves in noninstantaneous response nonlinear Kerr media,” Opt. Lett. 37, 2472–2474 (2012).

[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, “Emergence of spectral incoherent solitons through supercontinuum generation in photonic crystal fiber,” Phys. Rev. E 84, 066605 (2011).

[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, “Emergence of spectral incoherent solitons through supercontinuum generation in photonic crystal fiber,” Phys. Rev. E 84, 066605 (2011).

[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]

J. Fatome, S. Pitois, and G. Millot, “Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability,” Opt. Fiber Technol. 12, 243–250 (2006).

[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., doi:10.1016/2014.03.002 (to be published).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).

[CrossRef]

K. Nithyanandan and K. Porsezian, “Interplay between relaxation of nonlinear response and coupling coefficient dispersion in the instability spectra of dual core optical fiber,” Opt. Commun. 303, 46–55 (2013).

[CrossRef]

M. Onorato, A. R. Osborne, and M. Serio, “Modulation instability in crossing sea states: a possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96, 014503 (2006).

[CrossRef]

M. Onorato, A. R. Osborne, and M. Serio, “Modulation instability in crossing sea states: a possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96, 014503 (2006).

[CrossRef]

T. Hansson, D. Anderson, M. Lisak, V. E. Semenov, and U. Österberg, “Quasilinear evolution and saturation of the modulational instability of partially coherent optical waves,” Phys. Rev. A 78, 011807 (2008).

[CrossRef]

I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).

[CrossRef]

J. Garnier, G. Xu, S. Trillo, and A. Picozzi, “Incoherent dispersive shocks in the spectral evolution of random waves,” Phys. Rev. Lett. 111, 113902 (2013).

[CrossRef]

B. Kliber, C. Michel, J. Garnier, and A. Picozzi, “Temporal dynamics of incoherent waves in noninstantaneous response nonlinear Kerr media,” Opt. Lett. 37, 2472–2474 (2012).

[CrossRef]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, “Emergence of spectral incoherent solitons through supercontinuum generation in photonic crystal fiber,” Phys. Rev. E 84, 066605 (2011).

[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]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., doi:10.1016/2014.03.002 (to be published).

[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]

J. Fatome, S. Pitois, and G. Millot, “Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability,” Opt. Fiber Technol. 12, 243–250 (2006).

[CrossRef]

K. Nithyanandan and K. Porsezian, “Interplay between relaxation of nonlinear response and coupling coefficient dispersion in the instability spectra of dual core optical fiber,” Opt. Commun. 303, 46–55 (2013).

[CrossRef]

M. Centurion, M. A. Porter, Y. Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and D. Psaltis, “Modulational instability in nonlinearity-managed optical media,” Phys. Rev. A 75, 063804 (2007).

[CrossRef]

M. Centurion, M. A. Porter, Y. Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and D. Psaltis, “Modulational instability in nonlinearity-managed optical media,” Phys. Rev. A 75, 063804 (2007).

[CrossRef]

M. Centurion, M. A. Porter, Y. Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and D. Psaltis, “Modulational instability in nonlinearity-managed optical media,” Phys. Rev. A 75, 063804 (2007).

[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., doi:10.1016/2014.03.002 (to be published).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

C. Condit, M. A. Schmidt, P. St, J. Russel, and F. Biancalana, “Highly noninstantaneous solitons in liquid-core photonic crystal fibers,” Phys. Rev. Lett. 105, 263902 (2010).

[CrossRef]

V. V. Konotop and M. Salerno, “Modulational instability in Bose–Einstein condensates in optical lattices,” Phys. Rev. A 65, 021602 (2002).

[CrossRef]

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).

[CrossRef]

C. Condit, M. A. Schmidt, P. St, J. Russel, and F. Biancalana, “Highly noninstantaneous solitons in liquid-core photonic crystal fibers,” Phys. Rev. Lett. 105, 263902 (2010).

[CrossRef]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]

D. Kip, M. Soljacić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]

T. Hansson, D. Anderson, M. Lisak, V. E. Semenov, and U. Österberg, “Quasilinear evolution and saturation of the modulational instability of partially coherent optical waves,” Phys. Rev. A 78, 011807 (2008).

[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]

M. Onorato, A. R. Osborne, and M. Serio, “Modulation instability in crossing sea states: a possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96, 014503 (2006).

[CrossRef]

X. Liu, J. W. Haus, and S. M. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]

C.-S. Chou and M.-F. Shih, “Slow light achieved by non-instantaneous modulation instability,” J. Opt. A Pure Appl. Opt. 11, 105204 (2009).

[CrossRef]

D. Kip, M. Soljacić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).

[CrossRef]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

A. A. Canabarro, B. Santos, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Interplay of XPM and nonlinear response time in the modulational instability of copropagating optical pulses,” J. Opt. Soc. Am. B 27, 1878–1885 (2010).

[CrossRef]

G. L. da Silva, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Modulational instability in lossless fibers with saturable delayed nonlinear response,” J. Opt. Soc. Am. B 26, 183–188 (2009).

[CrossRef]

C. Condit, M. A. Schmidt, P. St, J. Russel, and F. Biancalana, “Highly noninstantaneous solitons in liquid-core photonic crystal fibers,” Phys. Rev. Lett. 105, 263902 (2010).

[CrossRef]

M. Stepić, A. Maluckov, M. Stojanović, F. Chen, and D. Kip, “Modulational instability and solitary waves in one-dimensional lattices with intensity-resonant nonlinearity,” Phys. Rev. A 78, 043819 (2008).

[CrossRef]

M. Stepić, A. Maluckov, M. Stojanović, F. Chen, and D. Kip, “Modulational instability and solitary waves in one-dimensional lattices with intensity-resonant nonlinearity,” Phys. Rev. A 78, 043819 (2008).

[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., doi:10.1016/2014.03.002 (to be published).

[CrossRef]

I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).

[CrossRef]

J. Garnier, G. Xu, S. Trillo, and A. Picozzi, “Incoherent dispersive shocks in the spectral evolution of random waves,” Phys. Rev. Lett. 111, 113902 (2013).

[CrossRef]

S. Trillo, S. Wabnitz, G. I. Stegeman, and E. M. Wright, “Parametric amplification and modulational instabilities in dispersive nonlinear directional couplers with relaxing nonlinearity,” J. Opt. Soc. Am. B 6, 889–900 (1989).

[CrossRef]

I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).

[CrossRef]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]

J. Garnier, G. Xu, S. Trillo, and A. Picozzi, “Incoherent dispersive shocks in the spectral evolution of random waves,” Phys. Rev. Lett. 111, 113902 (2013).

[CrossRef]

S. B. Cavalcanti, M. Yu, and G. P. Agrawal, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).

[CrossRef]

C.-S. Chou and M.-F. Shih, “Slow light achieved by non-instantaneous modulation instability,” J. Opt. A Pure Appl. Opt. 11, 105204 (2009).

[CrossRef]

S. Trillo, S. Wabnitz, G. I. Stegeman, and E. M. Wright, “Parametric amplification and modulational instabilities in dispersive nonlinear directional couplers with relaxing nonlinearity,” J. Opt. Soc. Am. B 6, 889–900 (1989).

[CrossRef]

C. Cambournac, H. Maillotte, E. Lantz, J. M. Dudley, and M. Chauvet, “Spatiotemporal behavior of periodic arrays of spatial solitons in a planar waveguide with relaxing Kerr nonlinearity,” J. Opt. Soc. Am. B 19, 574–585 (2002).

[CrossRef]

G. L. da Silva, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Modulational instability in lossless fibers with saturable delayed nonlinear response,” J. Opt. Soc. Am. B 26, 183–188 (2009).

[CrossRef]

A. A. Canabarro, B. Santos, I. Gleria, M. L. Lyra, and A. S. B. Sombra, “Interplay of XPM and nonlinear response time in the modulational instability of copropagating optical pulses,” J. Opt. Soc. Am. B 27, 1878–1885 (2010).

[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).

[CrossRef]

N. Da Dalt, C. De Angelis, G. F. Nalesso, and M. Santagiustina, “Dynamics of induced modulational instability in waveguides with saturable nonlinearity,” Opt. Commun. 121, 69–72 (1995).

[CrossRef]

X. Liu, J. W. Haus, and S. M. Shahriar, “Modulation instability for a relaxational Kerr medium,” Opt. Commun. 281, 2907–2912 (2008).

[CrossRef]

K. Nithyanandan and K. Porsezian, “Interplay between relaxation of nonlinear response and coupling coefficient dispersion in the instability spectra of dual core optical fiber,” Opt. Commun. 303, 46–55 (2013).

[CrossRef]

J. Fatome, S. Pitois, and G. Millot, “Measurement of nonlinear and chromatic dispersion parameters of optical fibers using modulation instability,” Opt. Fiber Technol. 12, 243–250 (2006).

[CrossRef]

M. J. Potasek, “Modulation instability in an extended nonlinear Schrödinger equation,” Opt. Lett. 12, 921–923 (1987).

[CrossRef]

J. Klinger, H. Martin, and Z. Chen, “Experiments on induced modulational instability of an incoherent optical beam,” Opt. Lett. 26, 271–273 (2001).

[CrossRef]

B. Kliber, C. Michel, J. Garnier, and A. Picozzi, “Temporal dynamics of incoherent waves in noninstantaneous response nonlinear Kerr media,” Opt. Lett. 37, 2472–2474 (2012).

[CrossRef]

T. Hansson, D. Anderson, M. Lisak, V. E. Semenov, and U. Österberg, “Quasilinear evolution and saturation of the modulational instability of partially coherent optical waves,” Phys. Rev. A 78, 011807 (2008).

[CrossRef]

S. B. Cavalcanti, M. Yu, and G. P. Agrawal, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995).

[CrossRef]

M. Centurion, M. A. Porter, Y. Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and D. Psaltis, “Modulational instability in nonlinearity-managed optical media,” Phys. Rev. A 75, 063804 (2007).

[CrossRef]

M. Stepić, A. Maluckov, M. Stojanović, F. Chen, and D. Kip, “Modulational instability and solitary waves in one-dimensional lattices with intensity-resonant nonlinearity,” Phys. Rev. A 78, 043819 (2008).

[CrossRef]

V. V. Konotop and M. Salerno, “Modulational instability in Bose–Einstein condensates in optical lattices,” Phys. Rev. A 65, 021602 (2002).

[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]

B. Kibler, C. Michel, A. Kudlinski, B. Barviau, G. Millot, and A. Picozzi, “Emergence of spectral incoherent solitons through supercontinuum generation in photonic crystal fiber,” Phys. Rev. E 84, 066605 (2011).

[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]

C. Condit, M. A. Schmidt, P. St, J. Russel, and F. Biancalana, “Highly noninstantaneous solitons in liquid-core photonic crystal fibers,” Phys. Rev. Lett. 105, 263902 (2010).

[CrossRef]

L. D. Carr and J. Brand, “Spontaneous soliton formation and modulational instability in Bose–Einstein condensates,” Phys. Rev. Lett. 92, 040401 (2004).

[CrossRef]

M. Onorato, A. R. Osborne, and M. Serio, “Modulation instability in crossing sea states: a possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96, 014503 (2006).

[CrossRef]

I. Velchev, R. Pattnaik, and J. Toulouse, “Two-beam modulation instability in noninstantaneous nonlinear media,” Phys. Rev. Lett. 91, 093905 (2003).

[CrossRef]

J. Garnier, G. Xu, S. Trillo, and A. Picozzi, “Incoherent dispersive shocks in the spectral evolution of random waves,” Phys. Rev. Lett. 111, 113902 (2013).

[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996).

[CrossRef]

M. Soljacić, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, “Modulation instability of incoherent beams in noninstantaneous nonlinear media,” Phys. Rev. Lett. 84, 467–470 (2000).

[CrossRef]

D. Kip, M. Soljacić, M. Segev, E. Eugenieva, and D. N. Christodoulides, “Modulation instability and pattern formation in spatially incoherent light beams,” Science 290, 495–498 (2000).

[CrossRef]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep., doi:10.1016/2014.03.002 (to be published).

[CrossRef]

G. Carbou and B. Hanouzet, “Relaxation approximation of the Kerr model for the impedance initial-boundary value problem,” in Proceedings of the 6th AIMS International Conference (2007), paper 212220.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).