Lie group classification and invariant solutions of mKdV equation with time-dependent coefficients |
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| Institution: | 1. School of Mechanical and Mining Engineering, The University of Queensland, QLD 4072, Australia;2. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, Ministry of Education, Tianjin University, Tianjin 300072, China;3. State Key Laboratory of Coal Resources and Safe Mining, China University of Mining & Technology, Xuzhou 221116, Jiangsu Province, China;4. Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Malaysia |
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| Abstract: | This paper studies the modified Korteweg–de Vries equation with time variable coefficients of the damping and dispersion using Lie symmetry methods. We carry out Lie group classification with respect to the time-dependent coefficients. Lie point symmetries admitted by the mKdV equation for various forms for the time variable coefficients are obtained. The optimal system of one-dimensional subalgebras of the Lie symmetry algebras are determined. These are then used to determine exact group-invariant solutions, including soliton solutions, and symmetry reductions for some special forms of the equations. |
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