New Rational Homoclinic Solution and Rogue Wave Solution for the Coupled Nonlinear Schrödinger Equation

2014 ◽  
Vol 69 (8-9) ◽  
pp. 441-445 ◽  
Author(s):  
Long-Xing Li ◽  
Jun Liu ◽  
Zheng-De Dai ◽  
Ren-Lang Liu
Keyword(s):  
Schrödinger Equation ◽  
Wave Solution ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Homoclinic Solution ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Rogue Wave Solution

In this work, the rational homoclinic solution (rogue wave solution) can be obtained via the classical homoclinic solution for the nonlinear Schrödinger (NLS) equation and the coupled nonlinear Schrödinger (CNLS) equation, respectively. This is a new way for generating rogue wave comparing with direct constructing method and Darboux dressing technique

The rogue wave of the nonlinear Schrödinger equation with self-consistent sources

2018 ◽  
Vol 32 (30) ◽  
pp. 1850367 ◽  
Author(s):  
Yehui Huang ◽  
Hongqing Jing ◽  
Runliang Lin ◽  
Yuqin Yao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Wave Solution ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Breather Solution ◽  
Rogue Wave Solution ◽  
Self Consistent

In this paper, we study the nonlinear Schrödinger equation with self-consistent sources, and obtain the rogue wave solution, the breather solution and their interactions by the generalized Darboux transformation. The dynamics of the rogue wave solution, the breather solution and their interactions are analyzed.

Study on Breather-Type Rogue Wave Based on Fourth-Order Nonlinear Schrödinger Equation

2014 ◽  
Author(s):  
Wenyue Lu ◽  
Jianmin Yang ◽  
Haining Lv ◽  
Xin Li
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
The Waves

Rogue wave is a kind of wave that possesses concentrated energy, strong nonlinear and enormous devastating. When it interacts with the deep-sea structures, the structure will suffer a serious threat, and it may even cause significant harm to the offshore staff and property. Studies on the mechanism of rogue wave are of great significance to the platform design and security. It is also one of the hot issues on the waves of hydrodynamic studies. Some breather-type solutions of NLS equation have been considered as prototypes of rogue waves in ocean. They can appear from smooth initial condition only with a certain disturb given by the exact solution of NLS. In this paper, we have numerically studied rogue waves based on fourth order nonlinear Schrödinger equation. We show that the peaks of the largest amplitude of the resulting waves can be described in terms of the Peregrine breather-type solution as the solution of NLS equation.

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