Bäcklund transformation, infinite conservation laws and periodic wave solutions to a generalized (2+1)-dimensional Boussinesq equation. (October 2016)

• Record Type: Journal Article
• Authors: Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Zhang, Tian-Tian
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 388
• Page End: 408
• Publication Date: 2016-10
• Subjects: The (2+1)-dimensional Boussinesq equation -- Bell's polynomials -- Bäcklund transformation -- Infinite conservation laws -- Periodic wave solution -- Soliton solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.01.019
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Under investigation in this paper is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the water wave interaction. By using Bell polynomials, a lucid and systematic approach is proposed to systematically study the integrability of the equation, including its bilinear representation, soliton solutions, periodic wave solutions, Bäcklund transformation and Lax pairs, respectively. Furthermore, by virtue of its Lax equations, the infinite conservation laws of the equation are also derived with the recursion formulas. Finally, the asymptotic behavior of periodic wave solutions is shown with a limiting procedure.