Qualitative Analysis and Asymptotics of Solutions of The GKP-Class Equations with Variable Dispersion

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 multidimensional 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.