Klein, Christian; Saut, Jean-Claude Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations. (English) Zbl 1253.35150 J. Nonlinear Sci. 22, No. 5, 763-811 (2012). Summary: We first review the known mathematical results concerning the Kadomtsev-Petviashvili type equations. Then we perform numerical simulations to analyze various qualitative properties of the equations: blow-up versus long time behavior, stability and instability of solitary waves. Cited in 35 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35B35 Stability in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 35B44 Blow-up in context of PDEs 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:Kadomtsev-Petviashvili equations; qualitative properties; blow-up; stability PDFBibTeX XMLCite \textit{C. 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