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Mathematical Problems in Engineering
Volume 2017, Article ID 5453941, 15 pages
Research Article

Hybrid Solutions of (3 + 1)-Dimensional Jimbo-Miwa Equation

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Correspondence should be addressed to Huanhe Dong; moc.621@gnodshtam

Received 20 July 2017; Accepted 28 September 2017; Published 28 November 2017

Academic Editor: Maria L. Gandarias

Copyright © 2017 Yong Zhang 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.


The rational solutions, semirational solutions, and their interactions to the ()-dimensional Jimbo-Miwa equation are obtained by the Hirota bilinear method and long wave limit. The hybrid solutions contain rogue wave, lump solution, and the breather solution, in which the breathers which are manifested as growing and decaying periodic line waves show different dynamics in different planes. Rogue waves are localized in time and are obtained theoretically as a long wave limit of breathers with indefinitely larger periods; they arise from a constant background at and then disappear in the constant background when time goes on. More importantly, the interactions between some hybrid solutions are demonstrated in detail by the three-dimensional figures, such as hybrid solution between the stripe soliton and breather and hybrid solution between stripe soliton and lump solution.