F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–114 (2011).

[CrossRef]

B. Guo and L. Ling, “Rogue wave, breathers and bright-dark-rogue solutions for the coupled Schrödinger equations,” Chin. Phys. Lett. 28, 110202 (2011).

[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).

[CrossRef]

S. Wabnitz and N. N. Akhmediev, “Efficient modulation frequency doubling by induced modulation instability,” Opt. Commun. 283, 1152–1154 (2010).

[CrossRef]

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Phys. D 238, 540–549 (2009).

[CrossRef]

O. C. Wright, “Dressing procedure for some homoclinic connections of the Manakov system,” Applied Math. Lett. 19, 1185–1190 (2006).

[CrossRef]

M. G. Forest and O. C. Wright, “An integrable model for stable: unstable wave coupling phenomena,” Phys. D 178, 173–189 (2003).

[CrossRef]

O. C. Wright, “The Darboux transformation of some Manakov systems,” Applied Math. Lett. 16, 647–652 (2003).

[CrossRef]

M. G. Forest, S. P. Sheu, and O. C. Wright, “On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrödinger systems,” Phys. Lett. A 266, 24–33(2000).

[CrossRef]

M. G. Forest, D. W. McLaughlin, D. J. Muraki, and O. C. Wright, “Nonfocusing instabilities in coupled, integrable nonlinear Schrödinger PDES,” J. Nonlinear Sci. 10, 291–331 (2000).

[CrossRef]

O. C. Wright and M. G. Forest, “On the Bäcklund-gauge transformation and homoclinic orbits of a coupled nonlinear Schrödinger system,” Phys. D 141, 104–116 (2000).

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).

[CrossRef]

N. N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Zh. Eksp. Teor. Fiz. 94, 159–170 (1988) [Sov. Phys. JETP 67, 89–95 (1988)].

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Mat. Fiz. 69, 189–194 (1986) [Theor. Mat. Phys. 69, 1089 (1986)].

[CrossRef]

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Zh. Eksp. Teor. Fiz. 89, 1542–1551 (1985) [Sov. Phys. JETP 62, 894–899 (1985)].

G. J. Roske, “Some nonlinear multiphase reactions,” Stud. Appl. Math. 55, 231–238 (1976).

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505–516 (1973) [Sov. Phys. JETP 38, 248–253 (1974)].

L. A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Zh. Eksp. Teor. Fiz. 58, 903–911 (1970) [Sov. Phys. JETP 31, 486–490 (1970)].

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. Part 1: theory,” J. Fluid Mech. 27, 417–430 (1967).

[CrossRef]

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 471–476 (1966) [JETP Lett. 3, 307–310 (1966)].

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).

[CrossRef]

S. Wabnitz and N. N. Akhmediev, “Efficient modulation frequency doubling by induced modulation instability,” Opt. Commun. 283, 1152–1154 (2010).

[CrossRef]

N. N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Zh. Eksp. Teor. Fiz. 94, 159–170 (1988) [Sov. Phys. JETP 67, 89–95 (1988)].

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Mat. Fiz. 69, 189–194 (1986) [Theor. Mat. Phys. 69, 1089 (1986)].

[CrossRef]

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Zh. Eksp. Teor. Fiz. 89, 1542–1551 (1985) [Sov. Phys. JETP 62, 894–899 (1985)].

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[CrossRef]

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. Part 1: theory,” J. Fluid Mech. 27, 417–430 (1967).

[CrossRef]

L. A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Zh. Eksp. Teor. Fiz. 58, 903–911 (1970) [Sov. Phys. JETP 31, 486–490 (1970)].

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 471–476 (1966) [JETP Lett. 3, 307–310 (1966)].

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[CrossRef]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–114 (2011).

[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).

[CrossRef]

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Zh. Eksp. Teor. Fiz. 89, 1542–1551 (1985) [Sov. Phys. JETP 62, 894–899 (1985)].

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi–Pasta–Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).

[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).

[CrossRef]

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. Part 1: theory,” J. Fluid Mech. 27, 417–430 (1967).

[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).

[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–114 (2011).

[CrossRef]

M. G. Forest and O. C. Wright, “An integrable model for stable: unstable wave coupling phenomena,” Phys. D 178, 173–189 (2003).

[CrossRef]

O. C. Wright and M. G. Forest, “On the Bäcklund-gauge transformation and homoclinic orbits of a coupled nonlinear Schrödinger system,” Phys. D 141, 104–116 (2000).

M. G. Forest, S. P. Sheu, and O. C. Wright, “On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrödinger systems,” Phys. Lett. A 266, 24–33(2000).

[CrossRef]

M. G. Forest, D. W. McLaughlin, D. J. Muraki, and O. C. Wright, “Nonfocusing instabilities in coupled, integrable nonlinear Schrödinger PDES,” J. Nonlinear Sci. 10, 291–331 (2000).

[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).

[CrossRef]

B. Guo and L. Ling, “Rogue wave, breathers and bright-dark-rogue solutions for the coupled Schrödinger equations,” Chin. Phys. Lett. 28, 110202 (2011).

[CrossRef]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi–Pasta–Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).

[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).

[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–114 (2011).

[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–114 (2011).

[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).

[CrossRef]

N. N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Zh. Eksp. Teor. Fiz. 94, 159–170 (1988) [Sov. Phys. JETP 67, 89–95 (1988)].

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Mat. Fiz. 69, 189–194 (1986) [Theor. Mat. Phys. 69, 1089 (1986)].

[CrossRef]

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Zh. Eksp. Teor. Fiz. 89, 1542–1551 (1985) [Sov. Phys. JETP 62, 894–899 (1985)].

B. Guo and L. Ling, “Rogue wave, breathers and bright-dark-rogue solutions for the coupled Schrödinger equations,” Chin. Phys. Lett. 28, 110202 (2011).

[CrossRef]

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505–516 (1973) [Sov. Phys. JETP 38, 248–253 (1974)].

M. G. Forest, D. W. McLaughlin, D. J. Muraki, and O. C. Wright, “Nonfocusing instabilities in coupled, integrable nonlinear Schrödinger PDES,” J. Nonlinear Sci. 10, 291–331 (2000).

[CrossRef]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).

[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–114 (2011).

[CrossRef]

G. Millot, “Multiple four-wave mixing-induced modulational instability in highly birefringent fibers,” Opt. Lett. 26, 1391–1393 (2001).

[CrossRef]

N. N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Zh. Eksp. Teor. Fiz. 94, 159–170 (1988) [Sov. Phys. JETP 67, 89–95 (1988)].

M. G. Forest, D. W. McLaughlin, D. J. Muraki, and O. C. Wright, “Nonfocusing instabilities in coupled, integrable nonlinear Schrödinger PDES,” J. Nonlinear Sci. 10, 291–331 (2000).

[CrossRef]

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Phys. D 238, 540–549 (2009).

[CrossRef]

G. J. Roske, “Some nonlinear multiphase reactions,” Stud. Appl. Math. 55, 231–238 (1976).

M. G. Forest, S. P. Sheu, and O. C. Wright, “On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrödinger systems,” Phys. Lett. A 266, 24–33(2000).

[CrossRef]

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 471–476 (1966) [JETP Lett. 3, 307–310 (1966)].

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi–Pasta–Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).

[CrossRef]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[CrossRef]

S. Wabnitz and N. N. Akhmediev, “Efficient modulation frequency doubling by induced modulation instability,” Opt. Commun. 283, 1152–1154 (2010).

[CrossRef]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16, 986–988 (1991).

[CrossRef]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).

[CrossRef]

O. C. Wright, “Dressing procedure for some homoclinic connections of the Manakov system,” Applied Math. Lett. 19, 1185–1190 (2006).

[CrossRef]

M. G. Forest and O. C. Wright, “An integrable model for stable: unstable wave coupling phenomena,” Phys. D 178, 173–189 (2003).

[CrossRef]

O. C. Wright, “The Darboux transformation of some Manakov systems,” Applied Math. Lett. 16, 647–652 (2003).

[CrossRef]

M. G. Forest, S. P. Sheu, and O. C. Wright, “On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrödinger systems,” Phys. Lett. A 266, 24–33(2000).

[CrossRef]

M. G. Forest, D. W. McLaughlin, D. J. Muraki, and O. C. Wright, “Nonfocusing instabilities in coupled, integrable nonlinear Schrödinger PDES,” J. Nonlinear Sci. 10, 291–331 (2000).

[CrossRef]

O. C. Wright and M. G. Forest, “On the Bäcklund-gauge transformation and homoclinic orbits of a coupled nonlinear Schrödinger system,” Phys. D 141, 104–116 (2000).

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Phys. D 238, 540–549 (2009).

[CrossRef]

L. A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Zh. Eksp. Teor. Fiz. 58, 903–911 (1970) [Sov. Phys. JETP 31, 486–490 (1970)].

O. C. Wright, “The Darboux transformation of some Manakov systems,” Applied Math. Lett. 16, 647–652 (2003).

[CrossRef]

O. C. Wright, “Dressing procedure for some homoclinic connections of the Manakov system,” Applied Math. Lett. 19, 1185–1190 (2006).

[CrossRef]

B. Guo and L. Ling, “Rogue wave, breathers and bright-dark-rogue solutions for the coupled Schrödinger equations,” Chin. Phys. Lett. 28, 110202 (2011).

[CrossRef]

T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. Part 1: theory,” J. Fluid Mech. 27, 417–430 (1967).

[CrossRef]

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).

[CrossRef]

M. G. Forest, D. W. McLaughlin, D. J. Muraki, and O. C. Wright, “Nonfocusing instabilities in coupled, integrable nonlinear Schrödinger PDES,” J. Nonlinear Sci. 10, 291–331 (2000).

[CrossRef]

N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Mat. Fiz. 69, 189–194 (1986) [Theor. Mat. Phys. 69, 1089 (1986)].

[CrossRef]

S. Wabnitz and N. N. Akhmediev, “Efficient modulation frequency doubling by induced modulation instability,” Opt. Commun. 283, 1152–1154 (2010).

[CrossRef]

G. Millot, “Multiple four-wave mixing-induced modulational instability in highly birefringent fibers,” Opt. Lett. 26, 1391–1393 (2001).

[CrossRef]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16, 986–988 (1991).

[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, “Peregrine soliton generation and breakup in standard telecommunications fiber,” Opt. Lett. 36, 112–114 (2011).

[CrossRef]

O. C. Wright and M. G. Forest, “On the Bäcklund-gauge transformation and homoclinic orbits of a coupled nonlinear Schrödinger system,” Phys. D 141, 104–116 (2000).

M. G. Forest and O. C. Wright, “An integrable model for stable: unstable wave coupling phenomena,” Phys. D 178, 173–189 (2003).

[CrossRef]

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Phys. D 238, 540–549 (2009).

[CrossRef]

M. G. Forest, S. P. Sheu, and O. C. Wright, “On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrödinger systems,” Phys. Lett. A 266, 24–33(2000).

[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011).

[CrossRef]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi–Pasta–Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).

[CrossRef]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).

[CrossRef]

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” Pis’ma Zh. Eksp. Teor. Fiz. 3, 471–476 (1966) [JETP Lett. 3, 307–310 (1966)].

G. J. Roske, “Some nonlinear multiphase reactions,” Stud. Appl. Math. 55, 231–238 (1976).

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz. 65, 505–516 (1973) [Sov. Phys. JETP 38, 248–253 (1974)].

N. N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “N-modulation signals in a single-mode optical waveguide under nonlinear conditions,” Zh. Eksp. Teor. Fiz. 94, 159–170 (1988) [Sov. Phys. JETP 67, 89–95 (1988)].

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Zh. Eksp. Teor. Fiz. 89, 1542–1551 (1985) [Sov. Phys. JETP 62, 894–899 (1985)].

L. A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Zh. Eksp. Teor. Fiz. 58, 903–911 (1970) [Sov. Phys. JETP 31, 486–490 (1970)].