Quasi-periodic wave solutions, soliton solutions, and integrability to a (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation

被引：23

作者：

Yan, Hui ^{[1
,2
]}

Tian, Shou-Fu ^{[1
,2
,3
,4
,5
]}

Feng, Lian-Li ^{[1
,2
]}

Zhang, Tian-Tian ^{[1
,2
]}

机构：

[1] China Univ Min & Technol, Dept Math, Xuzhou, Peoples R China

[2] China Univ Min & Technol, Ctr Nonlinear Equat, Xuzhou, Peoples R China

[3] China Univ Min & Technol, Key Lab Gas & Fire Control Coal Mines, Xuzhou, Peoples R China

[4] China Univ Min & Technol, Sch Safety Engn, Xuzhou, Peoples R China

[5] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge, England

来源：

WAVES IN RANDOM AND COMPLEX MEDIA | 2016年 / 26卷 / 04期

基金：

中国博士后科学基金;

关键词：

RATIONAL CHARACTERISTICS; EVOLUTION-EQUATIONS; SYMMETRIES;

D O I：

10.1080/17455030.2016.1166289

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, a (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko (gBK) equation is investigated, which can be used to describe the interaction of a Riemann wave propagating along y-axis and a long wave propagating along x-axis. The complete integrability of the gBK equation is systematically presented. By employing Bell's polynomials, a lucid and systematic approach is proposed to systematically study its bilinear formalism, bilinear Backlund transformations, Lax pairs, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic wave solutions and soliton solutions of the gBK equation are derived. Finally, an asymptotic relation between the periodic wave solutions and soliton solutions are strictly established under a certain limit condition.

引用

页码：444 / 457

页数：14

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