Construction of solitons of the Kadomtsev-Petviashvili equation

Abstract

Kadomtsev-Petviashvili equation describes the evolution of waves in shallow water, ion-acoustic waves, long waves in shear flows, and many other situations. This type of model equations describe the interaction between solitary waves and relevant in a number of problems in hydrodynamics, solid state physics, plasma physics, etc.

Among the known solutions of this equation - nonspreading eddies or vortices solitons (vortex is for environment in which its particles have an angular velocity of rotation about an axis). Solitons of this kind have been found theoretically and simulated in the laboratory, can spontaneously occur in planetary atmospheres. On the properties and conditions of existence of soliton-like a whirlwind of wonderful features of Jupiter's atmosphere - the Great Red Spot.

This article investigated the Kadomtsev-Petviashvili equation, which, in turn, is a multidimensional soliton. Using the method of Hirota were built soliton, two-soliton, three-soliton, four-soliton solutions of the Kadomtsev-Petviashvili equation. Shows graphs of soliton solutions for various parameters of time.

This scientific article is presented on pages 9, contains 6 points. This paper also presents seven graphs, built in the software package Maple 17.