Instability of solitary-wave solutions of the 3-dimensional Kadomtsev-Petviashvili equation

Advances in Differential Equations

Volumn 7, Issue 1, 2002, Pages 1-23

  Bona, Jerry L ^a   Liu, Yue ^b  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^b UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

[No Author keywords available]

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EID: 34249063076     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. T.B. Benjamin, The stability of solitary waves, Proc. Royal. Soc. London. Ser. A, 328 (1972), 153-183.
2. J.L. Bona, V.A. Dougalis, W.H. Mckinney, and O.A. Karakashian, Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation, Philos. Trans. Royal Soc. London Series A, 351 (1995), 107-164.
3. J.L. Bona, W.H. Mckinney, and J.M. Restrepo, Stable and unstable solitary-wave solutions of the generalized regularized long-wave equation, Nonlinear Sci., 10 (2000), 603-638.
4. J.L. Bona, P.E. Souganidis, and W.A. Strauss, Stability and instability of solitary waves of Korteweg-de Vries type, Proc. Royal Soc. London. Ser. A, 411 (1987), 395-412.
5. A. De Bouard and J.-C. Saut, Solitary waves of generalized Kadomtsev-Petviashvili equation, Ann. Inst. H. Poincaré, Anal. Nonlinéaire, 14 (1997), 211-236.
6. A. De Bouard, J.-C. Saut, Remarks on the stability of generalized KP solitary waves, Contemp. Math., 200, American Math. Soc. (1996), 75-84.
7. A. De Bouard and J.-C. Saut, Symmetries and decay of the generalized KP solitary waves, SIAM J. Math. Anal., 28 (1997), 1064-1085.
8. J. Bourgain, On the Cauchy problem for the Kadomtsev-Petviashvili equations, Geom. Funct. Anal., 3 (1993) 315-341.
9. M. Grillakis, J. Shatah, and W.A. Strauss, Stability theory of solitary waves in the presence of symmetry, J. Funct. Anal., 74 (1987), 160-197.
10. B.B. Kadomtsev and V.I. Petviashvili, On the stability of solitary waves in weakly dispersing media, Sov. Phy. Dokl., 15 (1970), 539-541.
11. E.A. Kuznetsov and S.K. Turitsyn, Two-and three-dimensional solitons in weakly dispersive media. Soviet Phys. JETP, 55 (1982), 844-847.
12. Yue Liu, Instability of solitary waves for generalized Boussinesq equations, J. Dynamics Diff. Eqs., 5 (1993), 537-558.
13. Yue Liu, Blow up and instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation, Transactions American Math. Soc., 353 (2001), 191-208.
14. Yue Liu, Strong instability of solitary-wave solutions to a Kadomtsev-Petviashvili equation in three dimensions, To appear in J. Diff. Eqs., (2001).
15. Yue Liu and Xiao-Ping Wang, Nonlinear stability of solitary waves of a generalized Kadomsev-Petviashvili equation, Comm. Math. Phys., 183 (1997), 253-266.
16. L.A. Mikhailovskaya and N.S. Erokhin, On the stability of large gradient vortices in plasma, International Conference on Plasma Physics, Kiev 1987, 2 (1989), 69-72.
17. L. Molinet, On the asymptotic behavior of solutions to the (generalized) Kadomsev-Petviashvili-Burgers equations, J. Diff. Eqs., 152 (1999), 30-74.
18. V.I. Petviashvili and V.V. Yan'kov, Solitons and turbulence, in B. B. Kadomtsev (ed.) Rev. Plasma Phys., XIV (1989), 1-62.
19. J.-C. Saut, Remarks on the generalized Kadomtsev-Petviashvili equations, Indiana Univ. Math. J., 42 (1993), 1011-1026.
20. J.-C. Saut, Recent results on the generalized Kadomtsev-Petviashvili equations, Acta Appl. Math., 39 (1995), 477-487.
21. J. Shatah and W.A. Strauss, Instability of nonlinear bound states, Comm. Math. Phys., 100 (1985), 173-190.
22. M.D. Spector and T. Miloh, Stability of nonlinear periodic internal waves in a deep stratified fluid, SIAM J. Appl. Math., 54 (1994), 688-707.
23. P.E. Souganidis and W.A. Strauss, Instability of a class of dispersive solitary waves, Proc. Royal. Soc. Edinburgh, Ser. A, 114 (1990), 195-212.
24. S. Turitsyn and G. Fal'kovich, Stability of magnetoelastic soliton and self-focusing of sound in antiferromagnet, Sov. Phys. JETP, 62 (1985), 146-152.
25. S. Ukai, Local solutions of the Kadomtsev-Petviashvili equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 36 (1989), 193-209.