Local existence in time of small solutions to the Davey-Stewartson systems
Annales de l'I.H.P. Physique théorique, Tome 65 (1996) no. 4, pp. 313-366.
@article{AIHPA_1996__65_4_313_0,
author = {Hayashi, Nakao},
title = {Local existence in time of small solutions to the Davey-Stewartson systems},
journal = {Annales de l'I.H.P. Physique th\'eorique},
pages = {313--366},
publisher = {Gauthier-Villars},
volume = {65},
number = {4},
year = {1996},
zbl = {0869.35083},
mrnumber = {1420706},
language = {en},
url = {http://archive.numdam.org/item/AIHPA_1996__65_4_313_0/}
}
Hayashi, Nakao. Local existence in time of small solutions to the Davey-Stewartson systems. Annales de l'I.H.P. Physique théorique, Tome 65 (1996) no. 4, pp. 313-366. http://archive.numdam.org/item/AIHPA_1996__65_4_313_0/

[1] J.M. Ablowitz and A.S. Fokas, On the inverse scattering transform of multidimensional nonlinear equations, J. Math. Phys., Vol. 25, 1984, pp. 2494-2505. | MR 751539 | Zbl 0557.35110

[2] J.M. Ablowitz and R. Haberman, Nonlinear evolution equations in two and three dimensions, Phys. Rev. Lett., Vol. 35, 1975, pp. 1185-1188. | MR 427866

[3] J.M. Ablowitz and A. Segur, Solitons and Inverse Scattering Transform, PA: SIAM, 1981. | MR 642018

[4] D. Anker and N.C. Freeman, On the soliton solutions of the Davey-Stewartson equation for long waves, Proc. R. Soc. A, Vol. 360, 1978, pp. 529-540. | MR 483961 | Zbl 0384.76016

[5] D.J. Benney and G.L. Roskes, Wave instabilities, Stud. Appl. Math., Vol. 48, 1969, pp. 377-385. | Zbl 0216.52904

[6] H. Chihara, The initial value problem for the elliptic-hyperboic Davey-Stewatson equation, preprint, 1995. | MR 1684172

[7] H. Cornille, Solutions of the generalized nonlinear Schrödinger equation in two spatial dimensions, J. Math. Phys., Vol. 20, 1979, pp. 199-209. | MR 517386 | Zbl 0425.35087

[8] A. Davey and K. Stewartson, On three-dimensional packets of surface waves, Proc. R. Soc. A., Vol. 338, 1974, pp. 101-110. | MR 349126 | Zbl 0282.76008

[9] V.D. Djordjevic and L.G. Redekopp, On two-dimendional packets of capillary-gravity waves, J. Fluid Mech., Vol. 79, 1977, pp. 703-714. | MR 443555 | Zbl 0351.76016

[10] S. Doi, On the Cauchy problem for Schrödinger type equations and regularity of solutions, J. Math. Kyoto Univ., Vol. 34, 1994, pp. 319-328. | MR 1284428 | Zbl 0807.35026

[11] A.S. Fokas and P.M. Santini, Recursion operators and bi-Hamiltonian structures in multidimensions I, Comm. Math. Phys., Vol. 115, 1988, pp. 375-419. | MR 931668 | Zbl 0674.35074

[12] A.S. Fokas and P.M. Santini, Recursion operators and bi-Hamiltonian structures in multidimensions II, Comm. Math. Phys., Vol. 115, 1988, pp. 449-474. | MR 937770 | Zbl 0706.35129

[13] A.S. Fokas and L.Y. Sung, On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations, Inverse Problems, Vol. 8, 1992, pp. 673-708. | MR 1185594 | Zbl 0768.35069

[14] J.M. Ghidaglia and J.C. Saut, On the initial value problem for the Davey-Stewartson systems, Nonlinearity, Vol. 3, 1990, pp. 475-506. | MR 1054584 | Zbl 0727.35111

[15] N. Hayashi and J.C. Saut, Global existence of small solutions to the Davey-Stewartson and the Ishimori sysytems, Diff. Integral Eqs., Vol. 8, 1995, pp. 1657-1675. | MR 1347974 | Zbl 0827.35120

[16] C.E. Kenig, G. Ponce and L. Vega, Oscillatory integral and rregularity of dispersive equations, Indiana Univ. J., Vol. 40, 1991, pp. 33-69. | MR 1101221 | Zbl 0738.35022

[17] C.E. Kenig, G. Ponce and L. Vega, Small solutions to nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Vol. 11, 1993, pp. 255-288. | Numdam | MR 1230709 | Zbl 0786.35121

[18] C.E. Kenig, G. Ponce and L. Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via contraction principle, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 527-620. | MR 1211741 | Zbl 0808.35128

[19] F. Linares and G. Ponce, On the Davey-Stewartson systems, Ann. Inst. Henri Poincaré, Anal. non linéaire, Vol. 10, 1993, pp. 523-548. | Numdam | MR 1249105 | Zbl 0807.35136

[20] R.S. Strichartz, Restriction of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., Vol. 44, 1977, pp. 705-714. | MR 512086 | Zbl 0372.35001

[21] L.Y. Sung, An inverse-scattering transform for the Davey-Stewartson II equations , Part III, J. Math. Anal. Appl., Vol. 183, 1994, pp. 477-494. | MR 1274849 | Zbl 0841.35106