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 theoreti-cally 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.