Modified Boussinesq System with Variable Coefficients: Classical Lie Approach and Exact Solutions

Journal of Partial Differential Equations
Vol. 22 No. 2 (2009), pp. 97-110
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Author(s)
    R. K. GUPTA
    Department of Applied Sciences and Humanities, Institute of Technology and Management, Sector 23-A, Gurgaon, Pin-122017 (Haryana), India.
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,
    K. SINGH
    Jaypee University of Information Technology, Waknaghat, P.O. Dumehar Bani, Kandaghat, Distt. Solan, Pin-173215 (H.P.), India.
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1 Department of Applied Sciences and Humanities, Institute of Technology and Management, Sector 23-A, Gurgaon, Pin-122017 (Haryana), India.
2 Jaypee University of Information Technology, Waknaghat, P.O. Dumehar Bani, Kandaghat, Distt. Solan, Pin-173215 (H.P.), India.
Received
January 31, 2007
Accepted
November 6, 2008
Abstract

The Lie-group formalism is applied to investigate the symmetries of the modified Boussinesq system with variable coefficients. We derived the infinitesimals and the admissible forms of the coefficients that admit the classical symmetry group. The reduced systems of ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.

Keywords
Lie symmetries;nonlinear diffusion;exact solutions;optimal system;reductions;global solutions;characteristic algebraic system
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