Breathers, quasi-periodic and travelling waves for a generalized -dimensional Yu-Toda-Sasa-Fukayama equation in fluids. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Hu, Wen-Qiang; Gao, Yi-Tian; Zhao, Chen; Jia, Shu-Liang; Lan, Zhong-Zhou
• Is Part Of: Waves in random and complex media. Volume 27:Issue 3(2017)
• Page Start: 458
• Page End: 481
• Publication Date: 2017-07-03
• Subjects: Electromagnetic waves -- Periodicals; Electromagnetic waves -- Scattering -- Periodicals; 531.1133
• DOI: 10.1080/17455030.2016.1262975
• Languages: English
• ISSNs: 1745-5030

Abstract

Abstract: Under investigation in this paper is a generalized -dimensional Yu–Toda–Sasa–Fukayama equation for the interfacial wave in a two-layer fluid or the elastic quasi-plane wave in a liquid lattice. By virtue of the binary Bell polynomials, bilinear form of this equation is obtained. With the help of the bilinear form, N -soliton solutions are obtained via the Hirota method, and a bilinear Bäcklund transformation is derived to verify the integrability. Homoclinic breather waves are obtained according to the homoclinic test approach, which is not only the space-periodic breather but also the time-periodic breather via the graphic analysis. Via the Riemann theta function, quasi one-periodic waves are constructed, which can be viewed as a superposition of the overlapping solitary waves, placed one period apart. Finally, soliton-like, periodical triangle-type, rational-type and solitary bell-type travelling waves are obtained by means of the polynomial expansion method.