Families of exact solutions of a new extended (2+1)-dimensional Boussinesq equation

Abstract

A new variant of the $(2+1)$-dimensional [$(2+1)d$] Boussinesq equation was recently introduced by J. Y. Zhu, arxiv:1704.02779v2, 2017; see eq. (3). First, we derive in this paper the one-soliton solutions of both bright and dark types for the extended $(2+1)d$ Boussinesq equation by using the traveling wave method. Second, $N$-soliton, breather, and rational solutions are obtained by using the Hirota bilinear method and the long wave limit. Nonsingular rational solutions of two types were obtained analytically, namely: (i) rogue-wave solutions having the form of W-shaped lines waves and (ii) lump-type solutions. Two generic types of semi-rational solutions were also put forward. The obtained semi-rational solutions are as follows: (iii) a hybrid of a first-order lump and a bright one-soliton solution and (iv) a hybrid of a first-order lump and a first-order breather.

arXiv commentAccepted by Nonlinear Dynamics, 19 pages including 10 figures

References in corpus (13)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
• Instabilities, breathers and rogue waves in optics
• General high-order rogue waves and their dynamics in the nonlinear Schroedinger equation
• A generating mechanism for higher order rogue waves
• Rogue waves in the Davey-Stewartson equation
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Dynamics of rogue waves in the Davey-Stewartson II equation
• Non-Gaussian statistics and extreme waves in a nonlinear optical cavity
• Breather and Rogue Wave solutions of a Generalized Nonlinear Schrodinger Equation
• Few-cycle optical rogue waves:complex modified Korteweg-de Vries equation
• Semi-rational solutions of the third-type Davey-Stewartson equation
• Line-soliton and rational solutions to (2+1)-dimensional Boussinesq equation by Dbar-problem

Cited by in corpus (2)

• Dynamics of Higher-order Bright and Dark Rogue Waves in a New (2+1)-Dimensional Integrable Boussinesq Model
• Painlevé Analysis and Higher-Order Rogue Waves of a Generalized(3+1)-dimensional Shallow Water Wave Equation