Lie symmetry analysis of the time-variable coefficient B-BBM equation

Motlatsi Molati,Chaudry Masood Khalique

doi:10.1186/1687-1847-2012-212

Motlatsi Molati, Chaudry Masood Khalique

Open Access

https://doi.org/10.1186/1687-1847-2012-212

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Abstract

We perform Lie group classification of a time-variable coefficient combined Burgers and Benjamin-Bona-Mahony equations (B-BBM equation). The direct analysis of the determining equations is employed to specify the forms of these time-dependent coefficients also known as arbitrary parameters. It is established that these model parameters have time-dependent functional forms of linear, power and exponential type.

Highlights

The Benjamin-Bona-Mahony equation, known as the regularized-long-wave equation [ ], ut + ux + uux – δuxxt =, ( )boasts a wide range of applications in the unidirectional propagation of weakly long dispersive waves in inviscid fluids
The Lie group classification is a systematic approach through which the parameters assume their forms naturally
3 Lie group classification This section deals with specifying the forms of the arbitrary parameters through the direct analysis of the classifying relations with the aim of extending the principal symmetry Lie algebra

Summary

Introduction

The direct method of group classification [ , ] is used to analyze the classifying relations, i.e., the equations which contain the arbitrary model parameters. We deduce the following from Eq ( ): If q = and h(t) = , we obtain the variable coefficient Burgers equation ut + f (t)uux + g(t)uxx = . The determining equations for the arbitrary elements (classifying relations) are generated in Section . – uqf (t)h(t)ηxxu + h(t)ηtxu = , ( )

Results

Conclusion