Analyticity of solitary wave solutions to generalized Kadomtsev-Petviashvili equations

Royal Society of Edinburgh - Proceedings A

Volumn 131, Issue 2, 2001, Pages 391-424

  Kato, Keiichi ^a   Pipolo, Patrick Nicolas ^a,b  

^a TOKYO UNIVERSITY OF SCIENCE   (Japan)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746959269     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500000925     Document Type: Article

References (27)

1. M. J. Ablowitz and P. A. Clarkson. Solitons, nonlinear evolution equation and inverse scattering, London Mathematical Society, Lecture Note Series, No. 149 (Cambridge University Press, 1991).
2. R. Adams. Sobolev spaces (Academic, 1975).
3. C. J. Amick and J. F. Toland. On solitary water waves of finite amplitude. Arch. Ration. Mech. Analysis. 76 (1981), 9-95.
4. O. V. Besov, V. P. Ilin and S. M. Nikolskii. Integral representations of functions and imbedding theorems, vol. 1 (Wiley, 1978).
5. J. L. Bona and H. Chen. Existence and asymptotic properties of solitary wave solutions of Benjamin type equation. Adv. Diff. Eqns 3(1) (1998), 51-84.
6. J. L. Bona and Y. A. Li. Decay and analyticity of solitary waves. J. Math. Pures Appliq. 76 (1997), 377-430.
7. J. Bourgain. On the Cauchy problem for the Kadomtsev-Petviashvili equations. Geometric Function. Analysis 3 (1993), 315-341.
8. T. Cazenave. An introduction to nonlinear Schrödinger equations. In Textes de Metodos Matematicos, vol. 26 (Rio de Janeiro: Instituto de Metematica-UFRJ, 1993).
9. A. de Bouard and J.-C. Saut. Remarks on the stability of generalized KP solitary waves. In Contemporary mathematics, vol. 200, pp. 75-84 (Providence, RI: American Mathematical Society, 1996).
10. A. de Bouard and J.-C. Saut. Symmetries and decay of the generalized Kadomtsev-Petviashvili solitary waves. SIAM J. Math. Analysis 24 (1997), 1064-1085.
11. A. de Bouard and J.-C. Saut. Solitary waves of generalized Kadomtsev-Petviashvili equations. Ann. Henri Inst. Poincarê Analyse Non Linéaire 14 (1997), 211-236.
12. A. de Bouard, N. Hayashi and K. Kato. Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations. Ann. Henri Inst. Poincarê Analyse Non Linéaire 12 (1995), 673-725.
13. A. Faminskii. The Cauchy problem for the Kadomtsev-Petviashvili equations. Russian Math. Surveys 5 (1990), 203-204.
14. A. Faminskii. The Cauchy problem for the Kadomtsev-Petviashvili equations. Siberian J. Math. 33 (1992), 133-143.
15. D. Gilbarg and N. Trudinger. Elliptic partial differential equations of second order (Springer, 1977).
16. A. Hasegawa and Y. Kodama. Solitons in optical communications, Oxford Series in Optical and Imaging Sciences, vol. 7 (Oxford: Clarendon, 1995).
17. K. Kato. New idea for proof of analyticity of solutions to analytic nonlinear elliptic equations. Sci. University Tokyo J. Math. 32 (1996), 157-161.
18. K. Kato and K. Taniguchi. Gevrey regularizing effect for nonlinear Schrödinger equations. Osaka J. Math. 33 (1996), 863-880.
19. P. L. Lions. The concentration-compactness principle in the calculus of variations, the locally compact case. I, II. Ann. Inst. Henri Poincaré Analyse Non Linéaire 1 (1984), 104-145, 223-283.
20. Y. Liu and X.-P. Wang. Nonlinear stability of solitary waves of a generalized Kadomtsev-Petviashvili equation. Commun. Math. Phys. 183 (1997), 252-266.
21. P.-N. Pipolo. Analyticity and smoothing effects for some nonlinear dispersive equations. PhD thesis (Science University of Tokyo, 1999).
22. W. Rudin. Real and complex analysis. Mathematics Series (McGraw-Hill, 1987).
23. J. C. Saut and N. Tzvetkov. The Cauchy problem for higher-order K.P. equations. J. Diff. Eqns 153 (1999), 196-222.
24. M. Tom. On a generalized Kadomtsev-Petviashvili equation. In Mathematical problems in the theory of water waves, AMS Contemporary Mathematics, vol. 200, pp. 193-210 (Providence, RI: American Mathematical Society, 1996).
25. S. Ukai. Local solutions of the Kadomtsev-Petviashvili equations. J. Fac. Sci. Univ. Tokyo 36 (1989), 193-209.
26. M. Willem. Minimax theorems. Progress in nonlinear differential equations and their applications, vol. 24 (Basel: Birkhauseur, 1997).
27. E. Zeidler. Nonlinear functional analysis and its application, vol. 3 (Springer, 1986).