# Exact solutions of nonlinear wave equations with power law nonlinearity

K. S. Al-Ghafri, E. V. Krishnan

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

The analytic solutions of nonlinear wave equations with power law nonlinearity have been investigated. We have applied the separation of variables and the auxiliary equation methods to three equations called the nonlinear dispersive equation, K(n+1;n+1) equation and K(n;n) equation. As a result, a wide range of travelling wave solutions have been obtained. Thus, the methods used here are efficient and can be applied to many nonlinear wave equations. The validation of all solutions is justified by using tools of computer algebra system.

Original language English 537-551 15 Nonlinear Studies 24 3 Published - 2017

### Fingerprint

Nonlinear Wave Equation
Wave equations
Power Law
Exact Solution
Nonlinearity
Nonlinear Dispersive Equations
Algebra
Auxiliary equation
Computer algebra system
Separation of Variables
Traveling Wave Solutions
Analytic Solution
Range of data

### Keywords

• Auxiliary equation method
• Exact solutions
• K(n+1;n+1) equation
• K(n;n) equation
• Nonlinear dispersive equation
• Separation of variables method

### ASJC Scopus subject areas

• Modelling and Simulation
• Applied Mathematics

### Cite this

In: Nonlinear Studies, Vol. 24, No. 3, 2017, p. 537-551.

Research output: Contribution to journalArticle

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AB - The analytic solutions of nonlinear wave equations with power law nonlinearity have been investigated. We have applied the separation of variables and the auxiliary equation methods to three equations called the nonlinear dispersive equation, K(n+1;n+1) equation and K(n;n) equation. As a result, a wide range of travelling wave solutions have been obtained. Thus, the methods used here are efficient and can be applied to many nonlinear wave equations. The validation of all solutions is justified by using tools of computer algebra system.

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