Approximate solutions of nonlinear PDEs by the invariant expansion |
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| Affiliation: | [1]Faculty of Science, Ningbo University, Ningbo 315211, China; [2]Center of Nonlinear Science, Ningbo University, Ningbo 315211, China |
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| Abstract: | It is difficult to obtain exact solutions of the nonlinear partial differential equations(PDEs) due to their complexity and nonlinearity,especially for non-integrable systems.In this paper,some reasonable approximations of real physics are considered,and the invariant expansion is proposed to solve real nonlinear systems.A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as the Korteweg-de Vries(KdV) equation with a fifth-order dispersion term,the perturbed fourth-order KdV equation,the KdV-Burgers equation,and a Boussinesq-type equation. |
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| Keywords: | approximate solution invariant expansion Mobious transformation invariance |
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