M. Ablowitz, D. Kaup, A. Newell, and H. Segur, The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems, Studies in Applied Mathematics, vol.34, issue.12, pp.249-315, 1974.
DOI : 10.1002/sapm1974534249

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De-angelis et al., Frequency Generation and Solitonic Decay in ThreeWave Interactions, Optics Express, vol.17, issue.16, pp.13889-13894, 2009.
DOI : 10.1364/OE.17.013889

R. Beals and R. Coifman, Inverse scattering and evolution equations, Communications on Pure and Applied Mathematics, vol.34, issue.1, pp.29-42, 1985.
DOI : 10.1002/cpa.3160380103

D. Chiron, On the Schrödinger approximation for wavetrains in semilinear equations

A. Craik, Wave interactions and fluid flows. Cambridge Monographs on Mechanics and Applied Mathematics, 1985.

D. Kaup, The inverse scattering solution for the full three dimensional three- wave resonant interaction, Physica D: Nonlinear Phenomena, vol.1, issue.1, pp.45-67, 1980.
DOI : 10.1016/0167-2789(80)90004-4

D. Kaup, A. Rieman, and A. Bers, Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium, Reviews of Modern Physics, vol.51, issue.2, pp.275-309, 1979.
DOI : 10.1103/RevModPhys.51.275

G. Schneider, Justification and failure of the nonlinear Schr??dinger equation in case of non-trivial quadratic resonances, Journal of Differential Equations, vol.216, issue.2, pp.354-386, 2005.
DOI : 10.1016/j.jde.2005.04.018

K. Yosida, Lectures on differential and integral equations, Pure and Applied Mathematics, 1960.

V. Zakharov, Exact solutions to the problem of the parametric interaction of three-dimensional wave packets, Dokl. Akad. Nauk. S.S.S.R. [Translated in Soviet Phys. Dokl, vol.228, issue.21, pp.1314-1316, 1976.

V. Zakharov, S. Manakov, and J. Lett, Resonant interaction of wave packets in nonlinear media. Zh. Eksp. Tero. Fiz. Pis'ma Red, pp.413-417, 1973.

V. Zakharov and S. Manakov, The theory of resonance interaction of wave packets in nonlinear media, Zh. Eksper. Teoret. Fiz. [Translated in Soviet Physics JETP, vol.69, issue.42 5, pp.1654-1673, 1975.

X. Zhou, Direct and inverse scattering transforms with arbitrary spectral singularities, Communications on Pure and Applied Mathematics, vol.20, issue.7, pp.895-938, 1989.
DOI : 10.1002/cpa.3160420702

X. Zhou, L2-Sobolev space bijectivity of the scattering and inverse scattering transforms, Communications on Pure and Applied Mathematics, vol.51, issue.7, pp.697-731, 1998.
DOI : 10.1002/(SICI)1097-0312(199807)51:7<697::AID-CPA1>3.0.CO;2-1