scholarly journals Solving localized wave solutions of the derivative nonlinear Schrödinger equation using an improved PINN method

2021 ◽  
Author(s):  
Juncai Pu ◽  
Jun Li ◽  
Yong Chen
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Derivative Nonlinear Schrödinger Equation

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.

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