Darboux transformation of a new generalized nonlinear Schrödinger equation: soliton solutions, breather solutions, and rogue wave solutions

2018 ◽  
Vol 92 (4) ◽  
pp. 2023-2036 ◽  
Author(s):  
Yaning Tang ◽  
Chunhua He ◽  
Meiling Zhou
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Wave Solutions ◽  
Rogue Wave Solutions ◽  
Generalized Nonlinear Schrödinger Equation

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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