Spectral Approach to Numerical In-tegration of the GKP or Belashov Class Equations in the Problems of Nonlinear Wave Dynamics Simulation

Abstract

The original method for numerical integration of the generalized Kadomtsev-Petviashvili (KP) equation which includes the term proportional to the fifth derivative (so called the Belashov-Karpman equation) which enables to study the solution's evolution and the multidimensional soliton's interaction's dynamics is presented. This method is rather simple in its computer realization and not such cumbersome comparatively with other known methods for the numerical integration of the different equations of the KP-class. In the paper we consider spectral approach to the numerical integration of the equations of the KP-class describing the dynamics of the ion-acoustic and magnetosonic waves in a plasma on the basis of the generalized KP equation. The method is rather simple in its computer realization and doesn't such cumbersome comparatively with other methods for the numerical integration of the differential equations of the KP-class, and very effective, so it doesn't require big time and memory expenditures. This approach was first used by us for study of some problems of nonlinear evolution of the fast magnetosonic (FMS) wave beam in magnetized plasma and can be generalized easily for all equations of the KP class