Abstract
By using Lie symmetry analysis and the method of dynamical systems for the extended mKdV equation, the all exact solutions based on the Lie group method are given. Especially, the bifurcations and traveling wave solutions are obtained. To guarantee the existence of the above solutions, all parameter conditions are determined. Furthermore, the exact analytic solutions are considered by using the power series method. Such solutions for the equation are important in both applications and the theory of nonlinear science.
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This work is supported by the Natural Science Foundation of China (No. 10671179 and No. 10771196), the Natural Science Foundation of Binzhou University (Bzxykj0806).
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Liu, H., Li, J. Lie Symmetry Analysis and Exact Solutions for the Extended mKdV Equation. Acta Appl Math 109, 1107–1119 (2010). https://doi.org/10.1007/s10440-008-9362-8
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DOI: https://doi.org/10.1007/s10440-008-9362-8
Keywords
- Lie symmetry analysis
- Bifurcation
- Traveling wave solution
- Exact analytic solution
- Extended mKdV equation