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.

Construction of dispersive optical solutions of the resonant nonlinear Schrödinger equation using two different methods

2018 ◽  
Vol 32 (33) ◽  
pp. 1850407 ◽  
Author(s):  
E. Tala-Tebue ◽  
Aly R. Seadawy
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Optical Fibers ◽  
Schrodinger Equation ◽  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Schrödinger ◽  
Exponential Function Method

The resonant nonlinear Schrödinger equation is studied in this work with the aid of two methods, namely the exponential rational function method and the modified exponential function method. This equation is used to describe the propagation of optical pulses in nonlinear optical fibers. Being concise and straightforward, these methods are used to build new exact analytical solutions of the model. The solutions obtained are not yet reported in the literature. The methods proposed can be extended to other types of nonlinear evolution equations in mathematical physics.

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 General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation

2012 ◽  
Vol 468 (2142) ◽  
pp. 1716-1740 ◽  
Author(s):  
Yasuhiro Ohta ◽  
Jianke Yang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
High Order ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Solution Dynamics ◽  
Free Parameters

General high-order rogue waves in the nonlinear Schrödinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the general N -th order rogue waves contain N −1 free irreducible complex parameters. In addition, the specific rogue waves obtained by Akhmediev et al. (Akhmediev et al. 2009 Phys. Rev. E 80 , 026601 ( doi:10.1103/PhysRevE.80.026601 )) correspond to special choices of these free parameters, and they have the highest peak amplitudes among all rogue waves of the same order. If other values of these free parameters are taken, however, these general rogue waves can exhibit other solution dynamics such as arrays of fundamental rogue waves arising at different times and spatial positions and forming interesting patterns.

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