scholarly journals Study on the generation mechanism of bright and dark solitary waves and rogue wave for a fourth-order dispersive nonlinear Schrödinger equation

2020 ◽  
Vol 69 (1) ◽  
pp. 010502
Author(s):  
Min Li ◽  
Bo-Ting Wang ◽  
Tao Xu ◽  
Juan-Juan Shui
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Solitary Waves ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Nonlinear Schrodinger Equation ◽  
Generation Mechanism ◽  
Nonlinear Schrödinger

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.

Breathers and Rogue Waves for the Fourth-Order Nonlinear Schrödinger Equation

2017 ◽  
Vol 72 (4) ◽  
pp. 339-344
Author(s):  
Yan Zhang ◽  
Yinping Liu ◽  
Xiaoyan Tang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

Abstract:In this article, a generalized Darboux transformation for the fourth-order nonlinear Schrödinger equation is constructed in terms of Darboux matrix method. Subsequently, breathers and the Nth-order rogue wave solutions of this equation are explicitly given in the light of the obtained Darboux transformation. Finally, we concretely discuss the dynamics of the obtained rogue waves, which are also demonstrated by some figures.

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