Characteristics of the breathers, rogue waves and solitary waves in a generalized (2+1)-dimensional Boussinesq equation
1 Department of Mathematics and Center of Nonlinear Equations, China University of Mining and Technology Xuzhou 221116, PRC
2 Department of Applied Mathematics and Theoretical Physics, University of Cambridge - Cambridge CB3 0WA, UK
Received: 4 June 2016
Accepted: 6 July 2016
Under investigation in this work is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the propagation of small-amplitude, long wave in shallow water. By virtue of Bell's polynomials, an effective way is presented to succinctly construct its bilinear form. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. Our results can be used to enrich the dynamical behavior of the generalized (2+1)-dimensional nonlinear wave fields.
PACS: 02.30.Ik – Integrable systems / 05.45.Yv – Solitons / 52.35.Mw – Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
© EPLA, 2016