Local existence in time of small solutions to the Davey-Stewartson systems
Annales de l'I.H.P. Physique théorique (1996)
- Volume: 65, Issue: 4, page 313-366
- ISSN: 0246-0211
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topHayashi, Nakao. "Local existence in time of small solutions to the Davey-Stewartson systems." Annales de l'I.H.P. Physique théorique 65.4 (1996): 313-366. <http://eudml.org/doc/76744>.
@article{Hayashi1996,
author = {Hayashi, Nakao},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Davey-Stewartson system; local existence in time},
language = {eng},
number = {4},
pages = {313-366},
publisher = {Gauthier-Villars},
title = {Local existence in time of small solutions to the Davey-Stewartson systems},
url = {http://eudml.org/doc/76744},
volume = {65},
year = {1996},
}
TY - JOUR
AU - Hayashi, Nakao
TI - Local existence in time of small solutions to the Davey-Stewartson systems
JO - Annales de l'I.H.P. Physique théorique
PY - 1996
PB - Gauthier-Villars
VL - 65
IS - 4
SP - 313
EP - 366
LA - eng
KW - Davey-Stewartson system; local existence in time
UR - http://eudml.org/doc/76744
ER -
References
top- [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. Zbl0557.35110MR751539
- [2] J.M. Ablowitz and R. Haberman, Nonlinear evolution equations in two and three dimensions, Phys. Rev. Lett., Vol. 35, 1975, pp. 1185-1188. MR427866
- [3] J.M. Ablowitz and A. Segur, Solitons and Inverse Scattering Transform, PA: SIAM, 1981. MR642018
- [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. Zbl0384.76016MR483961
- [5] D.J. Benney and G.L. Roskes, Wave instabilities, Stud. Appl. Math., Vol. 48, 1969, pp. 377-385. Zbl0216.52904
- [6] H. Chihara, The initial value problem for the elliptic-hyperboic Davey-Stewatson equation, preprint, 1995. MR1684172
- [7] H. Cornille, Solutions of the generalized nonlinear Schrödinger equation in two spatial dimensions, J. Math. Phys., Vol. 20, 1979, pp. 199-209. Zbl0425.35087MR517386
- [8] A. Davey and K. Stewartson, On three-dimensional packets of surface waves, Proc. R. Soc. A., Vol. 338, 1974, pp. 101-110. Zbl0282.76008MR349126
- [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. Zbl0351.76016MR443555
- [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. Zbl0807.35026MR1284428
- [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. Zbl0674.35074MR931668
- [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. Zbl0706.35129MR937770
- [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. Zbl0768.35069MR1185594
- [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. Zbl0727.35111MR1054584
- [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. Zbl0827.35120MR1347974
- [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. Zbl0738.35022MR1101221
- [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. Zbl0786.35121MR1230709
- [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. Zbl0808.35128MR1211741
- [19] F. Linares and G. Ponce, On the Davey-Stewartson systems, Ann. Inst. Henri Poincaré, Anal. non linéaire, Vol. 10, 1993, pp. 523-548. Zbl0807.35136MR1249105
- [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. Zbl0372.35001MR512086
- [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. Zbl0841.35106MR1274849
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