Exact solutions of a(2+1)-dimensional extended shallow water wave equation

作     者：Feng Yuan Jing-Song He Yi Cheng 袁丰;贺劲松;程艺

作者机构：School of Mathematical SciencesUniversity of Science and Technology of ChinaHefei 230026China Institute for Advanced StudyShenzhen UniversityShenzhen 518060China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2019年第28卷第10期

页      面：237-244页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11671219 and 11871446) 

主　　题：(2+1)-dimensional extended shallow water wave equation Hirota bilinear method dormion-type solution 

摘      要：We give the bilinear form and n-soliton solutions of a（2+1）-dimensional [（2+1）-D] extended shallow water wave（eSWW） equation associated with two functions v and r by using Hirota bilinear method. We provide solitons, breathers,and hybrid solutions of them. Four cases of a crucial φ（y）, which is an arbitrary real continuous function appeared in f of bilinear form, are selected by using Jacobi elliptic functions, which yield a periodic solution and three kinds of doubly localized dormion-type solution. The first order Jacobi-type solution travels parallelly along the x axis with the velocity（3k12+ α, 0） on（x, y）-plane. If φ（y） = sn（y, 3/10）, it is a periodic solution. If φ（y） = cn（y, 1）, it is a dormion-type-Ⅰ solutions which has a maximum（3/4）k1p1 and a minimum-（3/4）k1p1. The width of the contour line is ln■. If φ（y） = sn（y, 1）, we get a dormion-type-Ⅱ solution（26） which has only one extreme value-（3/2）k1p1. The width of the contour line is ln■. If φ（y） = sn（y, 1/2）/（1 + y2）, we get a dormion-type-Ⅲ solution（21） which shows very strong doubly localized feature on（x, y） plane. Moreover, several interesting patterns of the mixture of periodic and localized solutions are also given in graphic way.