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Advances in Mathematical Physics
Volume 2016, Article ID 7241625, 14 pages
http://dx.doi.org/10.1155/2016/7241625
Research Article

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

1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China
3Function Laboratory for Ocean Dynamics and Climate, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266237, China

Received 7 September 2016; Revised 25 October 2016; Accepted 10 November 2016

Academic Editor: Rita Traciná

Copyright © 2016 Hongwei Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The exact rational solutions, quasi-periodic wave solutions, and -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 -soliton solutions. At last, the interactions of the solitons are shown with the aid of -soliton solutions.