Nonlocal Symmetry and Explicit Solution of the Alice-Bob Modified Korteweg-de Vries Equation |
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| Authors: | Zheng-Yi Ma Jin-Xi Fei Jun-Chao Chen |
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| Institution: | 1. Department of Mathematics, Zhejiang Lishui University, Lishui 323000, China;
2. Department of Photoelectric Engineering, Zhejiang Lishui University, Lishui 323000, China;
3. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China |
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| Abstract: | Nonlocal symmetry and explicit solution of the integrable Alice-Bob modified Korteweg-de Vries (ABmKdV) equation is discussed, which has been established by the aid of the shifted parity and delayed time reversal to describe two-place events. Based on the Lax pair which contains the two-order partial derivative, the Lie symmetry group method is successfully applied to find the exact invariant solution for the AB-mKdV equation with nonlocal symmetry by introducing one suitable auxiliary variable. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to some specific functions are derived. Figures show the physical phenomenon, that is, "the shifted parity and delayed time reversal to describe two-place events". |
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| Keywords: | Alice-Bob modified Korteweg-de Vries equation Lax pair nonlocal symmetry explicit solution |
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