Solitary waves of generalized Kadomtsev-Petviashvili equations
de Bouard, Anne ; Saut, Jean-Claude
Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997), p. 211-236 / Harvested from Numdam
@article{AIHPC_1997__14_2_211_0,
     author = {de Bouard, Anne and Saut, Jean-Claude},
     title = {Solitary waves of generalized Kadomtsev-Petviashvili equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {14},
     year = {1997},
     pages = {211-236},
     mrnumber = {1441393},
     zbl = {0883.35103},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1997__14_2_211_0}
}
de Bouard, Anne; Saut, Jean-Claude. Solitary waves of generalized Kadomtsev-Petviashvili equations. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) pp. 211-236. http://gdmltest.u-ga.fr/item/AIHPC_1997__14_2_211_0/

[1] M.J. Ablowitz and P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, 1991. | MR 1149378 | Zbl 0762.35001

[2] M.J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, 1981. | MR 642018 | Zbl 0472.35002

[3] L.A. Abramyan and Y.A. Stepanyants, The structure of two-dimensional solitons in media with anomalously small dispersion, Sov. Phys. JETP, Vol. 61, 5, 1985, pp. 963-966.

[4] O.V. Besov, V.P. Il'In, S.M. Nikolskii, Integral Representations of Functions and Imbeddings Theorems, Vol. I, J. Wiley, 1978.

[5] J. Bourgain, On the Cauchy problem for the Kadomtsev-Petviashvili equations, Geometric and Functional Anal., Vol. 3, 4, 1993, pp. 315-341. | MR 1223434 | Zbl 0787.35086

[6] A. De Bouard, J.C. Saut, Sur les ondes solitaires des équations de Kadomtsev-Petviashvili, C. R. Acad. Sci. Paris, Vol. 320, série I , 1995, pp. 315-320. | MR 1320377 | Zbl 0833.35028

[7] A. Faminskii, The Cauchy problem for the Kadomtsev-Petviashvili equation, Russian Math. Surveys, Vol. 5, 1990, pp. 203-204 and Siberian J. Math., Vol. 33, 1992, pp. 133-143. | MR 1050944 | Zbl 0731.35089

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

[9] P. Isaza, J. Mejia and V. Stallhohm, Local solution for the Kadomtsev-Petviashvili equation in R2, J. Math. Anal. Appl., Vol. 196, 1995, pp. 566-587. | MR 1362707 | Zbl 0844.35107

[10] B.B. Kadomtsev and V.I. Petviashvili, On the stability of solitary waves in weakly dispersing media, Soviet Physics Doklady, Vol. 15, 6, 1970, pp. 539-541. | Zbl 0217.25004

[11] V.I. Karpman and V.Yu. Belashov, Dynamics of two-dimensional solitons in weakly dispersive media, Phys. Lett., A, Vol. 154, 1991, pp. 131-139.

[12] V.I. Karpman and V.Yu. Belashov, Evolution of three-dimensional nonlinear pulses in weakly dispersive media, Phys. Lett. A, Vol. 154, 1991, pp. 140-144.

[13] E.A. Kuznetsov, S.L. Musher, Effect of collapse of sound waves on the structure of collisionless shock waves in a magnetized plasma, Soviet Phys. JETP , Vol. 64, 5, 1986, pp. 947-955.

[14] P.L. Lions, The concentration-compactness principle in the calculus of variations, The locally compact case, I and II, Ann. I.H.P. Analyse Non Linéaire, Vol. I, 1984, pp. 104-145 and pp. 223-283. | Numdam | MR 778974 | Zbl 0704.49004

[15] P.I. Lizorkin, Multipliers of Fourier integrals, Proc. Steklov Inst. Math., Vol. 89, 1967, pp. 269-290. | MR 217519 | Zbl 0167.12404

[16] J. Pouget, Stability of nonlinear structures in a lattice model for phase transformations in alloys, Phys. Rev. B, Vol. 46, 1992, pp. 10554-10562.

[17] J.C. Saut, Remarks on the generalized Kadomtsev-Petviashvili equations, Indiana Math. J., Vol. 42, 3, 1993, pp. 1011-1026. | MR 1254130 | Zbl 0814.35119

[18] J.C. Saut, Recent results on the generalized Kadomtsev-Petviashvili equations, Acta Appl. Math.,, Vol. 39, 1995, pp. 477-487. | MR 1329578 | Zbl 0839.35121

[19] S. Ukai, Local solutions of the Kadomtsev-Petviashvili equation, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., Vol. 36, 1989, pp. 193-209. | MR 1014996 | Zbl 0703.35155

[20] X.P. Wang, M.J. Ablowitz and H. Segur, Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation, Physica D, Vol. 78, 1994, pp. 97-113. | MR 1302410 | Zbl 0824.35116

[21] X. Zhou, Inverse scattering transform for the time dependent Schrödinger equation with applications to the KP I equation, Comm. Math. Phys., Vol. 128, 1990, pp. 551-564. | MR 1045884 | Zbl 0702.35241

[22] M. Tom, On a generalized Kadomtsev-Petviashvili equation, in Mathematical Problems in the Theory of Water Waves, AMS Contemporary Mathematics, Vol. 200, 1996, pp. 193-210. | MR 1410508 | Zbl 0861.35103

[23] A. De Bouard, J.C. Saut, Symmetries and decay of the generalized KP Solitary waves, SIAM J. Math. Analysis, 1997. | Zbl 0889.35090

[24] A. De Bouard, J.C. Saut, Remarks on the Stability of generalized KP Solitary waves, in Mathematical Problems in the Theory of Water Waves, AMS Contemporary Mathematics, Vol. 200, 1996, pp. 75-84. | MR 1410501 | Zbl 0863.35095