L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1995.
DOI : 10.1063/1.2807623

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Self-Trapping of Partially Spatially Incoherent Light, Physical Review Letters, vol.77, issue.3, p.490, 1996.
DOI : 10.1103/PhysRevLett.77.490

M. Mitchell and M. Segev, Self-trapping of incoherent white light, Nature, vol.387, p.880, 1997.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, Z. Chen, and M. Segev, Theory of Incoherent Dark Solitons, Physical Review Letters, vol.80, issue.23, p.5113, 1998.
DOI : 10.1103/PhysRevLett.80.5113

Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Self-Trapping of Dark Incoherent Light Beams, Science, vol.280, issue.5365, p.889, 1998.
DOI : 10.1126/science.280.5365.889

N. N. Akhmediev and A. Ankiewicz, Coherent and Incoherent Contributions to Multisoliton Complexes, Phys. Rev. Lett, vol.83, p.4736, 1999.

M. Peccianti and G. Assanto, Incoherent spatial solitary waves in nematic liquid crystals, Optics Letters, vol.26, issue.22, p.1791, 2001.
DOI : 10.1364/OL.26.001791

G. A. Pasmanik, Self-interaction of incoherent light beams, Sov. Phys. JETP, vol.39, p.234, 1974.

M. Mitchell, M. Segev, T. Coskun, and D. N. Christodoulides, Theory of Self-Trapped Spatially Incoherent Light Beams, Physical Review Letters, vol.79, issue.25, p.4990, 1997.
DOI : 10.1103/PhysRevLett.79.4990

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Theory of Incoherent Self-Focusing in Biased Photorefractive Media, Physical Review Letters, vol.78, issue.4, p.646, 1997.
DOI : 10.1103/PhysRevLett.78.646

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

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Modulation Instability of Incoherent Beams in Noninstantaneous Nonlinear Media, Physical Review Letters, vol.84, issue.3, p.467, 2000.
DOI : 10.1103/PhysRevLett.84.467

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams, Science, vol.290, issue.5491, pp.495-498, 2000.
DOI : 10.1126/science.290.5491.495

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Statistical theory for incoherent light propagation in nonlinear media, Physical Review E, vol.65, issue.3, p.35602, 2002.
DOI : 10.1103/PhysRevE.65.035602

D. V. Dylov and J. W. Fleischer, Observation of All-Optical Bump-on-Tail Instability, Physical Review Letters, vol.100, issue.10, p.103903, 2008.
DOI : 10.1103/PhysRevLett.100.103903

P. Picozzi and M. Haelterman, Parametric Three-Wave Soliton Generated from Incoherent Light, Physical Review Letters, vol.86, issue.10, p.2010, 2001.
DOI : 10.1103/PhysRevLett.86.2010
URL : http://hdl.handle.net/2003/18547

A. Picozzi, C. Montes, and M. Haelterman, Coherence properties of the parametric three-wave interaction driven from an incoherent pump, Physical Review E, vol.66, issue.5, p.56605, 2002.
DOI : 10.1103/PhysRevE.66.056605

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, Incoherent Solitons in Instantaneous Response Nonlinear Media, Physical Review Letters, vol.92, issue.14, p.143906, 2004.
DOI : 10.1103/PhysRevLett.92.143906

M. Wu, P. Krivosik, B. A. Kalinikos, and C. E. Patton, Random Generation of Coherent Solitary Waves from Incoherent Waves, Physical Review Letters, vol.96, issue.22, p.227202, 2006.
DOI : 10.1103/PhysRevLett.96.227202

O. Cohen, H. Buljan, T. Schwartz, J. Fleischer, and M. Segev, Incoherent solitons in instantaneous nonlocal nonlinear media, Physical Review E, vol.73, issue.1, p.15601, 2006.
DOI : 10.1103/PhysRevE.73.015601

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, Incoherent spatial solitons in effectively instantaneous nonlinear media, Nature Photonics, vol.16, issue.6, p.371, 2008.
DOI : 10.1038/nphoton.2008.81

B. Alfassi, C. Rotschild, and M. Segev, Incoherent surface solitons in effectively instantaneous nonlocal nonlinear media, Physical Review A, vol.80, issue.4, p.41808, 2009.
DOI : 10.1103/PhysRevA.80.041808

A. Sauter, S. Pitois, G. Millot, and A. Picozzi, Incoherent modulation instability in instantaneous nonlinear Kerr media, Optics Letters, vol.30, issue.16, p.2143, 2005.
DOI : 10.1364/OL.30.002143

I. B. Bernstein, J. M. Green, and M. D. Kruskal, Exact Nonlinear Plasma Oscillations, Physical Review, vol.108, issue.3, p.546, 1957.
DOI : 10.1103/PhysRev.108.546

A. Hasegawa, Dynamics of an ensemble of plane waves in nonlinear dispersive media, Physics of Fluids, vol.18, issue.1, p.77, 1975.
DOI : 10.1063/1.860997

A. Hasegawa, Envelope soliton of random phase waves, Physics of Fluids, vol.20, issue.12, p.2155, 1977.
DOI : 10.1063/1.861822

V. E. Zakharov, S. L. Musher, and A. M. Rubenchik, Hamiltonian approach to the description of non-linear plasma phenomena, Physics Reports, vol.129, issue.5, pp.285-366, 1985.
DOI : 10.1016/0370-1573(85)90040-7

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, Physical Review E, vol.63, issue.3, p.35601, 2001.
DOI : 10.1103/PhysRevE.63.035601

M. Lisak, L. Helczynski, and D. Anderson, Relation between different formalisms describing partially incoherent wave propagation in nonlinear optical media, Optics Communications, vol.220, issue.4-6, p.321, 2003.
DOI : 10.1016/S0030-4018(03)01413-5

A. Picozzi, S. Pitois, and G. Millot, Spectral Incoherent Solitons: A Localized Soliton Behavior in the Frequency Domain, Physical Review Letters, vol.101, issue.9, p.93901, 2008.
DOI : 10.1103/PhysRevLett.101.093901
URL : https://hal.archives-ouvertes.fr/hal-00449133

B. Barviau, B. Kibler, A. Kudlinski, A. Mussot, G. Millot et al., Experimental signature of optical wave thermalization through supercontinuum generation in photonic crystal fiber, Optics Express, vol.17, issue.9, p.7392, 2009.
DOI : 10.1364/OE.17.007392
URL : https://hal.archives-ouvertes.fr/hal-00447573

Y. B. Zel-'dovich and R. A. Syunyaev, Shock wave structure in the radiation spectrum during Bose condensation of photons, Sov. Phys. JETP, vol.35, p.81, 1972.

Y. B. Zel-'dovich, E. V. Levich, and R. A. Syunyaev, Stimulated Compton interaction between Maxwellian electrons and spectrally narrow radiation, Sov. Phys. JETP, vol.35, p.733, 1972.

V. E. Zakharov, S. L. Musher, and A. M. Rubenchik, Weak Langmuir turbulence of an isothermal plasma, Sov. Phys. JETP, vol.42, p.80, 1976.

C. Montes, J. Peyraud, and M. Hénon, One-dimensional boson soliton collisions, Physics of Fluids, vol.22, issue.1, p.176, 1979.
DOI : 10.1063/1.862454

C. Montes, Photon soliton and fine structure due to nonlinear Compton scattering, Physical Review A, vol.20, issue.3, p.1081, 1979.
DOI : 10.1103/PhysRevA.20.1081

L. M. Nakhan-'kov, V. G. Rudakov, and L. , (16) should not be confused with the so-called 'Langmuir soliton'solutions of Zakharov-like equations, see e.g, Note that soliton solutions to the weak Langmuir turbulence kinetic Eq Degtyarev Dynamics of the formation and interaction of Langmuir solitons and strong turbulence

N. R. Pereira, Collisions between Langmuir solitons, Physics of Fluids, vol.20, issue.5, p.750, 1976.
DOI : 10.1063/1.861947

K. O. Abdulloev, I. L. Bogoljubskii, and V. G. Makhankov, Dynamics of Langmuir turbulence. Formation and interaction of solitons, Physics Letters A, vol.48, issue.3, p.161, 1974.
DOI : 10.1016/0375-9601(74)90523-4

B. Barviau, S. Randoux, and P. Suret, Spectral broadening of a multimode continuous-wave optical field propagating in the normal dispersion regime of a fiber, Optics Letters, vol.31, issue.11, p.1696, 2006.
DOI : 10.1364/OL.31.001696

A. Picozzi, Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics, Optics Express, vol.15, issue.14, p.9063, 2007.
DOI : 10.1364/OE.15.009063.m002
URL : https://hal.archives-ouvertes.fr/hal-00449113

A. Picozzi, Spontaneous polarization induced by natural thermalization of incoherent light, Optics Express, vol.16, issue.22, p.17171, 2008.
DOI : 10.1364/OE.16.017171
URL : https://hal.archives-ouvertes.fr/hal-00449130

A. Picozzi, Entropy and degree of polarization for nonlinear optical waves, Optics Letters, vol.29, issue.14, p.1653, 2004.
DOI : 10.1364/OL.29.001653

S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser, Journal of the Optical Society of America B, vol.24, issue.8, p.1729, 2007.
DOI : 10.1364/JOSAB.24.001729

S. A. Babin, V. Karalekas, E. Podivilov, V. Mezentsev, P. Harper et al., Turbulent broadening of optical spectra in ultralong Raman fiber lasers, Physical Review A, vol.77, issue.3, p.33803, 2008.
DOI : 10.1103/PhysRevA.77.033803

E. G. Turitsyna, G. Falkovich, V. K. Mezentsev, and S. K. Turitsyn, Optical turbulence and spectral condensate in long-fiber lasers, Physical Review A, vol.80, issue.3, p.31804, 2009.
DOI : 10.1103/PhysRevA.80.031804

A. Picozzi and S. Rica, Coherence absorption and condensation induced by thermalization of incoherent nonlinear fields, EPL (Europhysics Letters), vol.84, issue.3, p.34004, 2008.
DOI : 10.1209/0295-5075/84/34004

A. Picozzi and M. Haelterman, Condensation in Hamiltonian Parametric Wave Interaction, Physical Review Letters, vol.92, issue.10, p.103901, 2004.
DOI : 10.1103/PhysRevLett.92.103901

A. Picozzi and P. Aschieri, Influence of dispersion on the resonant interaction between three incoherent waves, Physical Review E, vol.72, issue.4, p.46606, 2005.
DOI : 10.1103/PhysRevE.72.046606

U. Bortolozzo, J. Laurie, S. Nazarenko, and S. Residori, Optical wave turbulence and the condensation of light, Journal of the Optical Society of America B, vol.26, issue.12, p.2280, 2009.
DOI : 10.1364/JOSAB.26.002280

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, Emergence of rogue waves from optical turbulence, Physics Letters A, vol.374, issue.34, p.3585, 2010.
DOI : 10.1016/j.physleta.2010.06.035
URL : https://hal.archives-ouvertes.fr/hal-00491491

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Velocity Locking of Incoherent Nonlinear Wave Packets, Physical Review Letters, vol.97, issue.3, p.33902, 2006.
DOI : 10.1103/PhysRevLett.97.033902
URL : https://hal.archives-ouvertes.fr/hal-00351114

S. Lagrange, H. R. Jauslin, and A. Picozzi, Thermalization of the dispersive three-wave interaction, Europhysics Letters (EPL), vol.79, issue.6, p.64001, 2007.
DOI : 10.1209/0295-5075/79/64001
URL : https://hal.archives-ouvertes.fr/hal-00449112

B. Barviau, B. Kibler, S. Coen, and A. Picozzi, Toward a thermodynamic description of supercontinuum generation, Optics Letters, vol.33, issue.23, p.2833, 2008.
DOI : 10.1364/OL.33.002833
URL : https://hal.archives-ouvertes.fr/hal-00447574

B. Barviau, B. Kibler, and A. Picozzi, Wave-turbulence approach of supercontinuum generation: Influence of self-steepening and higher-order dispersion, Physical Review A, vol.79, issue.6, p.63840, 2009.
DOI : 10.1103/PhysRevA.79.063840
URL : https://hal.archives-ouvertes.fr/hal-00447568

L. Levi, T. Schwartz, O. Manela, M. Segev, and H. Buljan, Spontaneous pattern formation upon incoherent waves: From modulation-instability to steady-state, Optics Express, vol.16, issue.11, p.7818, 2008.
DOI : 10.1364/OE.16.007818

V. E. Zakharov, V. S. L-'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I, 1992.
DOI : 10.1007/978-3-642-50052-7

K. Hasselmann, On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory, Journal of Fluid Mechanics, vol.7, issue.04, p.481, 1962.
DOI : 10.1017/S0022112062000373

K. Hasselmann, On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irrevesibility, Journal of Fluid Mechanics, vol.12, issue.02, p.273, 1963.
DOI : 10.1017/S0022112063000239

V. N. Tsytovich, Nonlinear Effects in Plasma, 1970.

A. Hasegawa, Plasma Instabilities and Nonlinear Effects, 1975.
DOI : 10.1007/978-3-642-65980-5

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schr??dinger equation, Physica D: Nonlinear Phenomena, vol.57, issue.1-2, p.96, 1992.
DOI : 10.1016/0167-2789(92)90090-A

V. E. Zakharov, F. Dias, and A. Pushkarev, One-dimensional wave turbulence, Physics Reports, vol.398, issue.1, p.1, 2004.
DOI : 10.1016/j.physrep.2004.04.002

D. J. Benney and P. G. Saffman, Nonlinear Interactions of Random Waves in a Dispersive Medium, Proc. R. Soc. London Ser. A 289, p.301, 1966.
DOI : 10.1098/rspa.1966.0013

A. C. Newell, The closure problem in a system of random gravity waves, Reviews of Geophysics, vol.9, issue.1, p.1, 1968.
DOI : 10.1029/RG006i001p00001

A. C. Newell, S. Nazarenko, and L. Biven, Wave turbulence and intermittency, Physica D: Nonlinear Phenomena, vol.152, issue.153, p.520, 2001.
DOI : 10.1016/S0167-2789(01)00192-0
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.522.8443

Y. V. Lvov and S. Nazarenko, Noisy spectra, long correlations, and intermittency in wave turbulence, Physical Review E, vol.69, issue.6, p.66608, 2004.
DOI : 10.1103/PhysRevE.69.066608

Y. Choi, Y. V. Lvov, and S. Nazarenko, Probability densities and preservation of randomness in wave turbulence, Physics Letters A, vol.332, issue.3-4, p.230, 2004.
DOI : 10.1016/j.physleta.2004.09.062

Y. Choi, Y. V. Lvov, and S. Nazarenko, Joint statistics of amplitudes and phases in wave turbulence, Physica D: Nonlinear Phenomena, vol.201, issue.1-2, p.121, 2005.
DOI : 10.1016/j.physd.2004.11.016

P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Anomalous Thermalization of Nonlinear Wave Systems, Physical Review Letters, vol.104, issue.5, p.54101, 2010.
DOI : 10.1103/PhysRevLett.104.054101
URL : https://hal.archives-ouvertes.fr/hal-00453105

C. Michel, P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, Influence of third-order dispersion on the propagation of incoherent light in optical fibers, Optics Letters, vol.35, issue.14, p.14, 2010.
DOI : 10.1364/OL.35.002367
URL : https://hal.archives-ouvertes.fr/hal-00696676

V. E. Zakharov and E. I. Schulman, Degenerative dispersion laws, motion invariants and kinetic equations, Physica D: Nonlinear Phenomena, vol.1, issue.2, p.192, 1980.
DOI : 10.1016/0167-2789(80)90011-1

V. E. Zakharov and E. I. Schulman, To the integrability of the system of two coupled nonlinear Schr??dinger equations, Physica D: Nonlinear Phenomena, vol.4, issue.2, p.270, 1982.
DOI : 10.1016/0167-2789(82)90068-9

V. E. Zakharov and E. I. Schulman, On additional motion invariants of classical Hamiltonian wave systems, Physica D: Nonlinear Phenomena, vol.29, issue.3, p.283, 1988.
DOI : 10.1016/0167-2789(88)90033-4

A. M. Balk and E. E. Ferapontov, Invariants of wave systems and web geometry, Nonlinear Waves and Weak Turbulence, 1998.
DOI : 10.1090/trans2/182/01

L. Bellac, M. Mortessagne, F. Batrouni, and G. , Equilibrium and Nonequilibrium, 2004.

A. S. Kompaneets, The establishment of thermal equilibrium between quanta and electrons, Zh. Eksp. Teor

A. A. Galeev, V. I. Karpman, and R. Z. Sagdeev, One Problem Now Under Solution in the Theory of Plasma Turbulence, Sov. Phys. Dokl, pp.1088-681, 1964.

Y. B. Zel-'dovich and E. V. Levich, Bose Condensation and Shock Waves in Photon Spectra

V. E. Zakharov, Collapse of Langmuir waves, Zh. Eksp. Teor. Fiz.Sov. Phys. JETP, vol.62, issue.35, pp.1745-1751, 1972.

H. Dreicer, Kinetic Theory of an Electron-Photon Gas, Physics of Fluids, vol.7, issue.5, p.735, 1964.
DOI : 10.1063/1.1711276

J. Garnier and A. Picozzi, Unified kinetic formulation of incoherent waves propagating in nonlinear media with noninstantaneous response, Physical Review A, vol.81, issue.3, p.33831, 2010.
DOI : 10.1103/PhysRevA.81.033831
URL : https://hal.archives-ouvertes.fr/hal-00473946

A. Picozzi and M. Haelterman, Hidden Coherence Along Space-Time Trajectories in Parametric Wave Mixing, Physical Review Letters, vol.88, issue.8, p.83901, 2002.
DOI : 10.1103/PhysRevLett.88.083901

O. Jedrkiewicz, A. Picozzi, M. Clerici, D. Faccio, D. Trapani et al., -Shaped Spatiotemporal Coherence in Optical Waves, Physical Review Letters, vol.97, issue.24, p.243903, 2006.
DOI : 10.1103/PhysRevLett.97.243903
URL : https://hal.archives-ouvertes.fr/ujm-01179915

R. Jordan, B. Turkington, and C. L. Zirbel, A mean-field statistical theory for the nonlinear Schr??dinger equation, Physica D: Nonlinear Phenomena, vol.137, issue.3-4, p.353, 2000.
DOI : 10.1016/S0167-2789(99)00194-3

R. Jordan and C. Josserand, Self-organization in nonlinear wave turbulence, Physical Review E, vol.61, issue.2, p.1527, 2000.
DOI : 10.1103/PhysRevE.61.1527

A. Eisner and B. Turkington, Nonequilibrium statistical behavior of nonlinear Schr??dinger equations, Physica D: Nonlinear Phenomena, vol.213, issue.1, p.85, 2006.
DOI : 10.1016/j.physd.2005.11.002

R. Rumpf and A. C. Newell, Coherent Structures and Entropy in Constrained, Modulationally Unstable, Nonintegrable Systems, Physical Review Letters, vol.87, issue.5, p.54102, 2001.
DOI : 10.1103/PhysRevLett.87.054102
URL : http://hdl.handle.net/2003/662

R. Rumpf and A. C. Newell, Localization and coherence in nonintegrable systems, Physica D: Nonlinear Phenomena, vol.184, issue.1-4, p.162, 2003.
DOI : 10.1016/S0167-2789(03)00220-3

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo, Free-Energy Transition in a Gas of Noninteracting Nonlinear Wave Particles, Physical Review Letters, vol.101, issue.4, p.44101, 2008.
DOI : 10.1103/PhysRevLett.101.044101

G. P. Agrawal, Nonlinear Fiber Optics, 2006.
DOI : 10.1007/3-540-46629-0_9

J. M. Dudley, G. Genty, and S. Coen, Supercontinuum generation in photonic crystal fiber, Reviews of Modern Physics, vol.78, issue.4, p.1135, 2006.
DOI : 10.1103/RevModPhys.78.1135
URL : https://hal.archives-ouvertes.fr/hal-00268071

M. J. Davis, S. A. Morgan, and K. Burnett, Simulations of Bose Fields at Finite Temperature, Physical Review Letters, vol.87, issue.16, p.160402, 2001.
DOI : 10.1103/PhysRevLett.87.160402

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, Condensation of Classical Nonlinear Waves, Physical Review Letters, vol.95, issue.26, p.263901, 2005.
DOI : 10.1103/PhysRevLett.95.263901

L. Biven, S. V. Nazarenko, and A. C. Newell, Breakdown of wave turbulence and the onset of intermittency, Physics Letters A, vol.280, issue.1-2, p.28, 2001.
DOI : 10.1016/S0375-9601(01)00016-0

G. Düring, A. Picozzi, and S. Rica, Breakdown of weak-turbulence and nonlinear wave condensation, Physica D: Nonlinear Phenomena, vol.238, issue.16, pp.1524-1549, 2009.
DOI : 10.1016/j.physd.2009.04.014

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov et al., Third-order dispersion for generating optical rogue solitons, Physics Letters A, vol.374, issue.4, p.691, 2010.
DOI : 10.1016/j.physleta.2009.11.058

A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay et al., Observation of extreme temporal events in CW-pumped supercontinuum, Optics Express, vol.17, issue.19, p.17010, 2009.
DOI : 10.1364/OE.17.017010.m001