Qualitative Analysis and Asymptotics of Solutions of the Gkp-Class Equations with Variable Dispersion

Belashov VYU and Belashova SE

Abstract

In this paper we study the dynamical systems associated with the generalized Kadomtsev-Petviashvili (GKP) equation with variable dispersion and consider the structure of possible multidi-mensional solutions and their asymptotics. We also present some considerations on constructing of the phase portraits of the systems in the 8-dimensional phase space for the GKP equation on the basis of the results of qualitative analysis of the generalized equations of the KdV-class.