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

doi:10.1088/1674-1056/ab3e65

中国物理B ›› 2019, Vol. 28 ›› Issue (10): 100202-100202.doi: 10.1088/1674-1056/ab3e65

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

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

Feng Yuan(袁丰), Jing-Song He(贺劲松), Yi Cheng(程艺)

1 School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China;
2 Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China

收稿日期:2019-07-14 修回日期:2019-08-13 出版日期:2019-10-05 发布日期:2019-10-05
通讯作者: Jing-Song He E-mail:hejingsong@szu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11671219 and 11871446).

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

Feng Yuan(袁丰)¹, Jing-Song He(贺劲松)², Yi Cheng(程艺)¹

1 School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China;
2 Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China

Received:2019-07-14 Revised:2019-08-13 Online:2019-10-05 Published:2019-10-05
Contact: Jing-Song He E-mail:hejingsong@szu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11671219 and 11871446).

摘要/Abstract

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)k₁p₁. 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.

关键词: (2+1)-dimensional extended shallow water wave equation, Hirota bilinear method, dormion-type solution

Abstract:

Key words: (2+1)-dimensional extended shallow water wave equation, Hirota bilinear method, dormion-type solution

中图分类号: (Integrable systems)

02.30.Ik

02.30.Jr (Partial differential equations) 05.45.-a (Nonlinear dynamics and chaos)

袁丰, 贺劲松, 程艺. Exact solutions of a (2+1)-dimensional extended shallow water wave equation[J]. 中国物理B, 2019, 28(10): 100202-100202.

Feng Yuan(袁丰), Jing-Song He(贺劲松), Yi Cheng(程艺). Exact solutions of a (2+1)-dimensional extended shallow water wave equation[J]. Chin. Phys. B, 2019, 28(10): 100202-100202.

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

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

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