Characteristics of rogue waves on a soliton background in a coupled nonlinear Schrödinger equation

Abstract

In this paper, a coupled nonlinear Schrödinger (CNLS) equation, which can describe evolution of localized waves in a two‐mode nonlinear fiber, is under investigation. By using the Darboux‐dressing transformation, the new localized wave solutions of the equation are well constructed with a detailed derivation. These solutions reveal rogue waves on a soliton background. Moreover, the main characteristics of the solutions are discussed with some graphics. Our results would be of much importance in predicting and enriching rogue wave phenomena in nonlinear wave fields.

Modulation instability, rogue waves and conservation laws in higher-order nonlinear Schrödinger equation

“…Based on the [27][28][29][30][31][32][33][34], the corresponding solution of the Lax pair can be sought in a new form…”

Novel Rogue Waves for a Mixed Coupled Nonlinear Schrödinger Equation on Darboux-Dressing Transformation

“…On the other hand, the Darboux-dressing transformation has been used in the study of the classical Schrödinger equation [17], integrable vector nonlinear Schrödinger equations [18], the Manakov system [23], the Kundu-nonlinear Schrödinger equation [25], the coupled cubic-quintic nonlinear Schrödinger equations [28] and in other fields [24,26,27,32].…”

Characteristics of rogue waves on a soliton background of the vector Lakshmanan‐Porsezian‐Daniel equation

“…The parameter scales the perturbation to a coupled NLS equation or Manakov system, 32,33 which only consider the group velocity dispersion and Kerr nonlinearity where q 1 ( x , t ) and q 2 ( x , t ) are complex valued functions. In the past decades, much work have been done for (): Chen and Mihalache used a nonrecursive Darboux transformation formalism to obtain the hierarchy of the rogue wave solution; 32 Wang and Han studied on rogue waves on a soliton background by the DDT method 33 …”