The stability of exact solitary wave solutions for simplified modified Camassa–Holm equation

2022 ◽  
pp. 106224
Author(s):  
XiaoHua Liu
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Holm Equation ◽  
The Stability

Quasi-soliton and other behaviour of the nonlinear cubic-quintic Schrödinger equation

1986 ◽  
Vol 64 (3) ◽  
pp. 311-315 ◽  
Author(s):  
Stuart Cowan ◽  
R. H. Enns ◽  
S. S. Rangnekar ◽  
Sukhpal S. Sanghera
Keyword(s):  
Solitary Wave ◽  
Schrödinger Equation ◽  
Parameter Space ◽  
Schrodinger Equation ◽  
Solitary Wave Solutions ◽  
Wave Interactions ◽  
Wave Solutions ◽  
The Stability

The stability of the solitary-wave solutions of the nonlinear cubic–quintic Schrödinger equation (NLCQSE) is examined numerically. The solutions are found not to be solitons, but quasi-soliton behaviour is found to persist over wide regions of parameter space. Outside these regions dispersive and explosive behaviour is observed in solitary-wave interactions.

scholarly journals A Note on Solitary Wave Solutions of the Nonlinear Generalized Camassa-Holm Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Lei Zhang ◽  
Xing Tao Wang
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Solitary Wave ◽  
Numerical Simulations ◽  
Solitary Wave Solutions ◽  
Simple Method ◽  
Wave Solutions ◽  
Holm Equation

We give a simple method for applying ordinary differential equation to solve the nonlinear generalized Camassa-Holm equation ut+2kux−uxxt+aumux−2uxuxx+uuxxx=0. Furthermore we give a new ansätz. In the cases where m=1,2,3, the numerical simulations demonstrate the results.

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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