Approximate symmetries and invariant solutions for the generalizations of the Burgers-Korteweg-de Vries model

Document Type : Research Article

Authors

1 Department of Mathematics, Payame Noor University, Tehran, Iran

2 School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

10.22060/miscj.2021.19554.5240

Abstract

In this paper the generalizations of the Burgers-Korteweg-de Vries model with small parameter derived by Kudryshov et al[ N.A. Kudryashov, D.I. Sinelshchikov. Extended models of non-linear waves in liquid with gas bubbles, International Journal of Non-Linear Mechanics 63 (2014) 31-38] is studied. A comprehensive study on the approximate symmetry analysis of the waves models is presented. First, we obtain approximate symmetry for the equation. Subsequently, in a physical application, using the first-order approximate symmetries, corresponding approximate invariant solutions to the perturbed non-linear models are obtained.
In this paper the generalizations of the Burgers-Korteweg-de Vries model with small parameter derived by Kudryshov et al[ N.A. Kudryashov, D.I. Sinelshchikov. Extended models of non-linear waves in liquid with gas bubbles, International Journal of Non-Linear Mechanics 63 (2014) 31-38] is studied. A comprehensive study on the approximate symmetry analysis of the waves models is presented. First, we obtain approximate symmetry for the equation. Subsequently, in a physical application, using the first-order approximate symmetries, corresponding approximate invariant solutions to the perturbed non-linear models are obtained.
In this paper the generalizations of the Burgers-Korteweg-de Vries model with small parameter derived by Kudryshov et al[ N.A. Kudryashov, D.I. Sinelshchikov. Extended models of non-linear waves in liquid with gas bubbles, International Journal of Non-Linear Mechanics 63 (2014) 31-38] is studied. A comprehensive study on the approximate symmetry analysis of the waves models is presented. First, we obtain approximate symmetry for the equation.

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