scholarly journals On the stability of solitary wave solutions of the fifth-order KdV equation

1997 ◽  
Vol 233 (1-2) ◽  
pp. 58-62 ◽  
Author(s):  
A.V. Buryak ◽  
A.R. Champneys
Keyword(s):  
Solitary Wave ◽  
Kdv Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Stability ◽  
Fifth Order

THE STABILITY OF THE SOLITARY WAVE SOLUTIONS TO THE GENERALIZED COMPOUND KDV EQUATION

2011 ◽  
Vol 04 (03) ◽  
pp. 475-480
Author(s):  
Xiaohua Liu ◽  
Weiguo Zhang
Keyword(s):  
Solitary Wave ◽  
Variational Method ◽  
Wave Solution ◽  
Lyapunov Functional ◽  
Solitary Wave Solution ◽  
Kdv Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Stability ◽  
Lyapunov Sense

Using variational method, we investigate that the solitary wave solution u(x - ct) to the Generalized Compound Kdv Equation with two nonlinear terms is stable in the Lyapunov sense when 0 < p < 2 holds. The result is new. There shows a new method to consider the extremum of Lyapunov functional.

The study of complexitons and periodic solitary-wave solutions with fifth-order KdV equation in (2+1) dimensions

2019 ◽  
Vol 33 (33) ◽  
pp. 1950411 ◽  
Author(s):  
Muhammad Tahir ◽  
Aziz Ullah Awan
Keyword(s):  
Solitary Wave ◽  
Bilinear Form ◽  
Kdv Equation ◽  
Three Dimensional ◽  
Solitary Wave Solutions ◽  
Test Technique ◽  
Wave Solutions ◽  
Complexiton Solutions ◽  
Hirota’S Bilinear Form ◽  
Fifth Order

In this paper, the generalized fifth-order (2[Formula: see text]+[Formula: see text]1)-dimensional KdV equation is scrutinized via the extended homoclinic test technique (EHTT) and extended transformed rational function (ETRF) method. With the aid of Hirota’s bilinear form, various exact solutions comprising, periodic solitary-wave, kinky-periodic solitary-wave, periodic soliton and complexiton solutions are constructed. Moreover, the mechanical features and dynamic characteristics of the obtained solutions are presented by three-dimensional plots.

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.

Exact Solitary-wave Solutions for the General Fifth-order Shallow Water-wave Models

1999 ◽  
Vol 54 (3-4) ◽  
pp. 272-274
Author(s):  
Woo-Pyo Hong ◽  
Young-Dae Jung
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Model Parameters ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Special Cases ◽  
Wave Models ◽  
Fifth Order

We perform a computerized symbolic computation to find some general solitonic solutions for the general fifth-order shal-low water-wave models. Applying the tanh-typed method, we have found certain new exact solitary wave solutions. The pre-viously published solutions turn out to be special cases with restricted model parameters.

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