Sur le problème de Cauchy pour des équations de type KP
Thèses d'Orsay, no. 565 (1999) , 182 p. 
@phdthesis{BJHTUP11_1999__0565__P0_0,
     author = {Tzvetkov, Nikolay},
     title = {Sur le probl\`eme de {Cauchy} pour des \'equations de type {KP}},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {565},
     year = {1999},
     language = {fr},
     url = {http://www.numdam.org/item/BJHTUP11_1999__0565__P0_0/}
}
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Tzvetkov, Nikolay. Sur le problème de Cauchy pour des équations de type KP. Thèses d'Orsay, no. 565 (1999), 182 p. http://numdam.org/item/BJHTUP11_1999__0565__P0_0/

[1] M. Abramowitz, I.A. Stegun, Handbook of mathematical functions, Dover (1965). | MR

[2] L.A. Abramyan, Y.A. Stepanyants, The structure of two-dimensional solitons in media with anomalously small dispersion, Sov. Phys. JETP, 61 (1985), 963-966.

[3] J. Albert, J. Bona, J.C. Saut, Model equations for waves in stratified fluids, Proc. Royal Soc. London A, 453 (1997), 1213-1260. | MR | Zbl | DOI

[4] J.M. Ash, J. Cohen, G. Wang, On strongly interacting internal solitary waves, J. Fourier Anal. and Appl. 5 (1996), 507-517. | MR | Zbl

[5] M. Ben-Artzi, J.-C. Saut, Uniform decay estimates for a class of oscillatory integrals and applications, Diff. Int. Eq. 12, (1999), 137-145. | MR | Zbl

[6] Besov, Ilin, Nikolski, Integral representation of functions and embedding theorems, J. Wiley, 1978. | MR

[7] B. Birnir, C. Kenig, G. Ponce, N. Svanstedt, L. Vega, On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations, Annales I.H.P., Analyse non linéaire 13 (1996), 529-535.

[8] B. Birnir, G. Ponce, N. Svanstedt, The local ill-posedness of the modified KdV equation, J. London Math. Soc. 53 (1996), 551-559. | MR | Numdam

[9] J. Bona, G. Ponce, J.C. Saut, M. Tom, A model system for strong interaction between internal solitary waves, Comm. Math. Phys. 143 (1992), 287-313. | MR | Zbl | DOI

[10] A. De Bouard, J.C. Saut, Solitary waves of generalized Kadomtsev-Petviashvili equations, Annales I.H.P., Analyse non linéaire 14 (1997), 211-236. | MR | Zbl | Numdam

[11] A. De Bouard, J.C. Saut, Symmetries and decay of the generalized KP solitary waves, SIAM J. Math. Anal. 28 (1997), 1064-1085. | MR | Zbl

[12] J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations I. Schrödinger equations, GAFA 3 (1993), 107-156. | MR | Zbl

[13] J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and application to nonlinear evolution equations II. The KdV equation, GAFA 3 (1993), 209-262. | MR | Zbl

[14] J. Bourgain, On the Cauchy problem for the Kadomtsev-Petviashvili equation, GAFA 3 (1993), 315-341. | MR | Zbl

[15] J. Bourgain, Periodic Korteweg de Vries equation with measures as initial data, Sel. Math. New. Ser. 3 (1997), 115-159. | MR | Zbl | DOI

[16] J. Bourgain, Refinements of Strichartz' inequality and applications to 2D-NLS with critical non-linearity, IMRN No.5 (1998), 253-283. | MR | Zbl | DOI

[17] J. Bourgain, Global well-posedness of defocusing critical nonlinear Scrödinger equation in the radial case, J. AMS (1999), 145-271. | MR | Zbl

[18] R. Coifman, Y. Meyer, Au delà des operateurs pseudodifférentiels, Asterisque 57, Societe Mathematique de France (1978). | MR | Zbl | Numdam

[19] J. Colliander, G. Staffilani, H. Takaoka Global well posedness of KdV below L2, Preprint (1998). | MR | Zbl

[20] A.V. Faminski, The Cauchy problem for the Kadomtsev-Petviashvili equation, Russian Math. Sur. 5 (1990), 203-204. | Zbl | MR | DOI

[21] G. Fonseca, F. Lineares, G. Ponce Global well-posedness for the Modified KdV equation, Comm. PDE, 24 (1999), 683-705. | MR | Zbl | DOI

[22] J.A. Gear, R. Grimshaw, Weak and strong interactions between internal solitary waves, Stud. Appl. Math. 65 (1984), 235-258. | MR | Zbl

[23] J. Ginibre, Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace (d'après Bourgain), Séminaire Bourbaki n. 796, Astérisque 237 (1996), 163-187. | MR | Zbl | Numdam

[24] J. Ginibre, Y. Tsutsumi, G. Velo, On the Cauchy problem for the Zakharov system, J. Funct. Anal., 151 (1997), 384-436. | MR | Zbl | DOI

[25] R. Grimshaw, Y. Zhu, Oblique interactions between internal solitary waves, Stud. Appl. Math. 92 (1994) 249-270. | MR | Zbl

[26] M. Haragus, Model equations for water waves in the presence of surface tension, Eur. J. Mech. B/Fluids, 15, 4 (1996), 471-492. | MR | Zbl

[27] M. Haragus-Courcelle, A. Ill'Ichev, Three dimensional solitary waves in the presence of additional surface effects, Eur. J. Mech. B/Fluids, 17 (1998). | MR | Zbl | DOI

[28] J.K. Hunter, J. Scheurle, Existence of perturbed solitary waves to a model equation for water waves, Physica D, 32 (1988), 253-268. | MR | Zbl

[29] A. Ill'Ichev, Self-channeling of surface water waves in the presence of an additional surface pressure, Preprint (1998). | Zbl

[30] A.T. Il'Ichev, A. Yu. Semenov, Stability of solitary waves in dispersive medias described by a fifth-order evolution equation, Theoret. Comput. Fluid Dynamics, 3 (1992), 307-326. | Zbl | DOI

[31] R.J. Iório Jr., W.V.L. Nunes, On equations of KP-type, Proc. Roy. Soc. Edinburgh A, 128 (1998), 725-743. | MR | Zbl | DOI

[32] P. Isaza, J. Mejia, V. Stallbohm, El problema de Cauchy para la ecuacion de Kadomtsev-Petviashvili (KP-II) en espacios de Sobolev, H s , s > 0 , Preprint (1998).

[33] B.B. Kadomtsev, V.I. Petviashvili, On the stability of solitary waves in weakly dispersive media, Soviet Phys. Dokl. 15 (1970), 539-541. | Zbl

[34] V.I. Karpman, Transverse stability of Kawahara solitons, Phys. Rev. E, 47, 1 (1993), 674-676. | DOI

[35] V.I. Karpman, V. Yu. Belashov, Dynamics of two dimensional solitons in weakly dispersive media, Phys. Lett. A 154 (1991), 131-139. | DOI

[36] V.I. Karpman, V. Yu. Belashov, Evolution of three-dimensional nonlinear pulses in weakly dispersive media, Phys. Lett. A 154 (1991), 140-144. | DOI

[37] T. Kato, On the Cauchy problem for the (generalized) Korteweg-de Vries equations, Advances in Mathematics, Suplementary Studies, Stud. Appl. Math., 8 (1983), 93-128. | MR | Zbl

[38] T. Kawahara, Oscillatory solitary waves in dispersive media, J. Phys. Soc. Japan, 33, 1, (1972), 260-264. | DOI

[39] C. Kenig, G. Ponce, L. Vega, On the (generalized) Korteweg-de Vries equation, Duke Math. J., 59 (1989), 585-610. | MR | Zbl | DOI

[40] C. E. Kenig, G. Ponce, L. Vega, Well-posedness of the initial value problem for the Korteweg-de Vries equation, J. AMS, 4 (1991), 323-347. | MR | Zbl

[41] C. E. Kenig, G. Ponce, L. Vega, The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices, Duke Math. J., 71 (1993), 1-21. | MR | Zbl | DOI

[42] C. Kenig, G. Ponce, L. Vega, A bilinear estimate with applications to the KdV equations, J. AMS, 9 (1996), 573-603. | MR | Zbl

[43] C. Kenig, G. Ponce, L. Vega, Quadratic forms for 1 - D semilinear Schrödinger equation, Trans. Amer. Math. Soc., 348 (1996), 3323-3353. | MR | Zbl | DOI

[44] S.N. Kruzhkov, A.V. Faminski, Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation, Math. U.S.S.R. Sbornik 48 (1984), 93-138. | Zbl

[45] F. Linares, L2 global well-posedness of the initial value problem associated to the Benjamin equation, J. Diff. Equations, 152 (1999), 377-393. | MR | Zbl | DOI

[46] A.V. Marchenko, Long waves in shallow liquid under ice cover, PMM USSR, 52, 2 (1998), 180-183. | Zbl

[47] L. Molinet, On the asymptotic behaviour of solutions to the (generalized) Kadomtsev-Petviashvili-Burgers equations, J. Diff. Eq. 152 (1999), 30-74. | MR | Zbl | DOI

[48] J.C. Saut, Remarks on the generalized Kadomtsev-Petviashvili equations, Indiana Univ. Math. J. 42 (1993), 1017-1029. | MR | Zbl

[49] J.C. Saut, N. Tzvetkov, The Cauchy problem for higher order KP equations, J. Diff. Eq. 153 (1999), 196-222. | MR | Zbl | DOI

[50] J.C. Saut, N. Tzvetkov, The Cauchy problem for the fifith order KP equations, Preprint (1999). | MR | Zbl

[51] R. Strichartz, Restriction of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J., 44 (1977), 705-714. | MR | Zbl | DOI

[52] H. Takaoka, Well-posedness for the Kadomtsev-Petviashvili II equation, Preprint (1998). | Zbl

[53] H. Takaoka, Global well-posedness for the Kadomtsev-Petviashvili II equation, Discrete Contin. Dynam. Systems (to appear). | MR | Zbl

[54] H. Takaoka, N. Tzvetkov, On the local regularity of Kadomtsev-Petviashvili II equation, Preprint (1999). | MR | Zbl

[55] M.M. Tom, On a generalized Kadomtsev-Petviashvili equation, Contemporary Mathematics A.M.S. 200 (1996), 193-210. | MR | Zbl

[56] N. Tzvetkov, Remarque sur la régularité locale de l'équation de Kadomtsev-Petviashvili, C.R. Acad. Sci. Paris, t. 326, Série I, 709-712, 1998. | MR | Zbl | DOI

[57] N. Tzvetkov, On the Cauchy problem for Kadomtsev-Petviashvili equations, Comm. PDE, 24 (1999), 1367-1397. | MR | Zbl | DOI

[58] N. Tzvetkov, Global low regularity solutions for Kadomtsev-Petviashvili equation, Diff. Int. Eq. (to appear). | MR | Zbl

[59] N. Tzvetkov, Remark on the local ill-posedness for KdV equation, C.R. Acad. Sd. Paris (to appear). | MR | Zbl

[60] S. Ukai, Local solutions of the Kadomtsev-Petviashvili equation, J. Fac. Soc. Univ. Tokyo Sect. I A Math., 36 (1989), 193-209. | MR | Zbl

[61] M.V. Wickerhauser, Inverse scattering for the heat operator and evolution in 2 + 1 variables, Comm. Math. Phys., 108 (1987), 67-87. | MR | Zbl | DOI