The Rational Solutions and Quasi-Periodic Wave Solutions as well as Interactions of N-Soliton Solutions for 3 + 1 Dimensional Jimbo-Miwa Equation

Abstract

The exact rational solutions, quasi-periodic wave solutions, and N-soliton solutions of 3 + 1 dimensional Jimbo-Miwa equation are acquired, respectively, by using the Hirota method, whereafter the rational solutions are also called algebraic solitary waves solutions and used to describe the squall lines phenomenon and explained possible formation mechanism of the rainstorm formation which occur in the atmosphere, so the study on the rational solutions of soliton equations has potential application value in the atmosphere field; the soliton fission and fusion are described based on the resonant solution which is a special form of the N-soliton solutions. At last, the interactions of the solitons are shown with the aid of N-soliton solutions.