Integrable decompositions for the (2+1)-dimensional Gardner equation |
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Authors: | Tao Xu Bo Tian Hai-Qiang Zhang Juan Li |
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Institution: | 1. School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, 100876, Beijing, China 2. State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, 100191, Beijing, China 3. Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications Ministry of Education, 100876, Beijing, China
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Abstract: | In this paper, with the computerized symbolic computation, the nonlinearization technique of Lax pairs is applied to find the integrable decompositions for the (2+1)-dimensional Gardner (2+1)-DG] equation. First, the mono-nonlinearization leads a single Lax pair of the (2+1)-DG equation to a generalized Burgers hierarchy which is linearizable via the Hopf–Cole transformation. Second, by the binary nonlinearization of two symmetry Lax pairs, the (2+1)-DG equation is decomposed into the generalized coupled mixed derivative nonlinear Schrödinger (CMDNLS) system and its third-order extension. Furthermore, the Lax representation and Darboux transformation for the CMDNLS and third-order CMDNLS systems are constructed. Based on the two integrable decompositions, the resonant N-shock-wave solution and an upside-down bell-shaped solitary-wave solution are obtained and the relevant propagation characteristics are discussed through the graphical analysis. |
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