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

• 来源期刊: 中国物理B（英文版）
• 关键词: (2+1)-dimensional extended shallow water wave equation Hirota bilinear method dormion-type solution
• 年，卷（期）: 2019,（10）
• 页码范围: 264-272
• 页数: 9页
• 语种: 英文
• DOI: 10.1088/1674-1056/ab3e65

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[(2 + √6 + √2 + √3)/(2 + √6-√2-√3)].If φ (y) =sn(y,1),we get a dormion-type-Ⅱ solution (26) which has only one extreme value-(3/2)kl pl.The width of the contour line is ln[(√2 + 1) / (√2-1)].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.