Exact solution via the spectral transform of a generalization with linearlyx-dependent coefficients of the nonlinear Schrödinger equation

1978 ◽  
Vol 22 (10) ◽  
pp. 420-424 ◽  
Author(s):  
F. Calogero ◽  
A. Degasperis
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Spectral Transform

Slowly varying solitary waves. II. Nonlinear Schrödinger equation

1979 ◽  
Vol 368 (1734) ◽  
pp. 377-388 ◽  
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Multiple Scale ◽  
Perturbation Parameter ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Scale Method

The slowly varying solitary wave is constructed as an asymptotic solution of the variable coefficient nonlinear Schrodinger equation. A multiple scale method is used to determine the amplitude and phases of the wave to the second order in the perturbation parameter. The method is similar to that used in (I) (R. Grimshaw 1979 Proc. R. Soc. Lond . A 368, 359). The results are interpreted by using conservation laws. Outer expansions are introduced to remove non-uniformities in the expansion. Finally, when the coefficients satisfy a certain constraint, an exact solution is constructed.

scholarly journals The exact solution of the nonlinear Schrödinger equation by the exp-function method

2021 ◽  
pp. 88-88
Author(s):  
Qiaoling Chen ◽  
Zhiqiang Sun
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Function Method ◽  
Solution Process ◽  
Nonlinear Schrodinger Equation ◽  
Dinger Equation ◽  
Nonlinear Schrödinger ◽  
Free Parameters

This paper elucidates the main advantages of the exp-function method in finding the exact solution of the nonlinear Schr?dinger equation. The solution process is extremely simple and accessible, and the obtained solution contains some free parameters.

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