scholarly journals Exact solitary and periodic wave solutions of high-order nonlinear Schrödinger equation and their relationship with Hamilton energy

AIP Advances ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 085212
Author(s):  
Weiguo Zhang ◽  
Yuli Guo ◽  
Siyu Hong ◽  
Xingqian Ling
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Wave ◽  
Nonlinear Schrodinger Equation ◽  
High Order ◽  
Periodic Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Hamilton Energy ◽  
Wave Solutions

CONSTRUCTING 2N-SOLITON PERIODIC WAVE SOLUTIONS FOR GENERALIZED DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION

2010 ◽  
Vol 21 (09) ◽  
pp. 1149-1168
Author(s):  
SHOU-FU TIAN ◽  
HONG-QING ZHANG
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Wave ◽  
Nonlinear Schrodinger Equation ◽  
Generalized Derivative ◽  
Periodic Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Derivative Nonlinear Schrödinger Equation

In this paper, three new kinds of N-fold Darboux transformations with multi-parameters for spectral problem associated with generalized Derivative Nonlinear Schrödinger equation (GDNS) are structured with the help of different gauge transformations. With these transformations, some new 2N-soliton periodic wave solutions for the GDNS equation are obtained by taking position spectral (λ > 0), negaton spectral (λ < 0) and complexiton spectral. When N = 1 we obtained two-soliton periodic wave solutions. In particular, when N = 2 we obtained some four-soliton periodic wave solutions. By using mathematical software, we show their profiles. In this method, we can give a Darboux transformation for a very systematic system of even-dimensional and odd-dimensional Lax integrable systems. This method can also be applied to other nonlinear evolution equations.

scholarly journals Exact Solutions for (2+1)-dimensional Nonlinear Schrödinger Equation Based on Modified Extended tanh Method

2019 ◽  
pp. 15-27
Author(s):  
Wang Juan ◽  
Wang Yudi ◽  
Xu Qian
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Wave ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Extended Tanh Method ◽  
Wave Solutions ◽  
Tanh Method

In this paper, modified extended tanh method is used to construct more general exact solutions of a (2+1)-dimensional nonlinear Schrödinger equation. With the aid of Maple and Matlab software, we obtain exact explicit kink wave solutions, peakon wave solutions, periodic wave solutions and so on and their images.

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