scholarly journals Implicit Solitary Waves for One of the Generalized Nonlinear Schrödinger Equations

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3024
Author(s):  
Nikolay A. Kudryashov
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Implicit Function ◽  
Solitary Wave Solutions ◽  
Independent Variables ◽  
Wave Solutions ◽  
New Form ◽  
Transformation Of Variables

Application of transformations for dependent and independent variables is used for finding solitary wave solutions of the generalized Schrödinger equations. This new form of equation can be considered as the model for the description of propagation pulse in a nonlinear optics. The method for finding solutions of equation is given in the general case. Solitary waves of equation are obtained as implicit function taking into account the transformation of variables.

Stability of solitary wave solutions of simultaneous nonlinear Schrödinger equations

1982 ◽  
Vol 28 (3) ◽  
pp. 379-383 ◽  
Author(s):  
J. C. Bhakta ◽  
M. R. Gupta
Keyword(s):  
Solitary Wave ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Solitary Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Different Types ◽  
The Stability

The stability of localized solitary wave solutions of simultaneous nonlinear Schrödinger equations describing different types of interacting waves in a plasma has been investigated. It is found that the stability depends on the nature and strength of the interaction potential between the two waves. The possible results of interactions between two colliding solitary waves have been discussed using the conservation laws.

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