de Bouard, Anne; Saut, Jean-Claude Symmetries and decay of the generalized Kadomtsev-Petviashvili solitary waves. (English) Zbl 0889.35090 SIAM J. Math. Anal. 28, No. 5, 1064-1085 (1997). Summary: We prove that the solitary waves of the generalized Kadomtsev-Petviashvili equations, when they exist, are cylindrical with respect to the transverse variables and decay with an optimal algebraic rate. Cited in 46 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35B40 Asymptotic behavior of solutions to PDEs 35Q51 Soliton equations Keywords:Kadomtsev-Petviashvili equations; solitary waves; symmetry; decay PDFBibTeX XMLCite \textit{A. de Bouard} and \textit{J.-C. Saut}, SIAM J. Math. Anal. 28, No. 5, 1064--1085 (1997; Zbl 0889.35090) Full Text: DOI