Rogue wave solutions for the generalized fifth-order nonlinear Schrödinger equation on the periodic background

Wave Motion ◽  
2021 ◽  
pp. 102839
Author(s):  
Zijia Wang ◽  
Zhaqilao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Rogue Wave Solutions ◽  
Fifth Order

Nonlinear Stage of Modulation Instability for a Fifth-Order Nonlinear Schrödinger Equation

2017 ◽  
Vol 72 (11) ◽  
pp. 1071-1075 ◽  
Author(s):  
Hui-Xian Jia ◽  
Dong-Ming Shan
Keyword(s):  
Phase Shift ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Rogue Wave ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Fifth Order

AbstractIn this article, a fifth-order nonlinear Schrödinger equation, which can be used to characterise the solitons in the optical fibre and inhomogeneous Heisenberg ferromagnetic spin system, has been investigated. Akhmediev breather, Kuzentsov soliton, and generalised soliton have all been attained via the Darbox transformation. Propagation and interaction for three-type breathers have been studied: the types of breather are determined by the module and complex angle of parameter ξ; interaction between Akhmediev breather and generalised soliton displays a phase shift, whereas the others do not. Modulation instability of the generalised solitons have been analysed: a small perturbation can develop into a rogue wave, which is consistent with the results of rogue wave solutions.

Breather and rogue wave solutions of an extended nonlinear Schrödinger equation with higher-order odd and even terms

2018 ◽  
Vol 32 (26) ◽  
pp. 1850309 ◽  
Author(s):  
Dan Su ◽  
Xuelin Yong ◽  
Yanjiao Tian ◽  
Jing Tian
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Spectral Parameters ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Rogue Wave Solutions

In this paper, an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms is investigated in detail. The equation for the one-dimensional magnetic systems is integrable and admits exact solutions. It is more accurate than the nonlinear Schrödinger equation in describing wave propagation in the ocean and optical fibers. First, the modulation instability of solutions is analyzed in the presence of small perturbation. Second, breather and rogue wave solutions of this equation are constructed via the modified Darboux transformation method. The effects of the higher-order terms are investigated graphically. Specially, the interactions between two breathers are studied by adjusting the spectral parameters and the collisions between breather and rogue waves are also discussed.

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