Journal of Physics & Astronomy

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


Affiliations
1 Kazan (Volga Region), Federal University, Kazan, Russian Federation
2 Kazan National Research Technical University Named after A.N. Tupolev, Kazan, Russian Federation
 

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.

Keywords

Dynamical System, Generalized KDV Equation, GKP Equation, Multidimensional Solutions, Phase Space, Qualitative Analysis, Solitons, Structure of Solutions, Variable Dispersion.
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  • Qualitative Analysis and Asymptotics of Solutions of the Gkp-Class Equations with Variable Dispersion

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Authors

V. Y. U. Belashov
Kazan (Volga Region), Federal University, Kazan, Russian Federation
S. E. Belashova
Kazan National Research Technical University Named after A.N. Tupolev, Kazan, Russian Federation

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.

Keywords


Dynamical System, Generalized KDV Equation, GKP Equation, Multidimensional Solutions, Phase Space, Qualitative Analysis, Solitons, Structure of Solutions, Variable Dispersion.

References