N-solitons, breathers and rogue waves for a generalized Boussinesq equation

Abstract

A particular attention is paid on a generalized nonlinear Boussinesq equation which can be used to describe the wave dynamics in fluids. Via symbolic computation method, analytical N-soliton solutions, three types of breather solutions (namely, Kuznetsov-Ma, Akhmediev and generalized breather solutions), and rogue wave solutions are obtained. The extreme points of rogue waves are analyzed in detail. Furthermore, a type of novel X-like soliton is observed.

Keywords:

• Generalized Boussinesq equation
• symbolic computation method
• N-soliton
• breather
• rogue wave
• interaction and collision

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 30D35
• 34A05
• 37K40
• 35Q35

Disclosure statement

No potential conflict of interest was reported by the author.