Lie symmetries and nonlocally related systems of the continuous and discrete dispersive long waves system by geometric approach |
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Authors: | Shou-Fu Tian Pan-Li Ma |
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Affiliation: | 1. Department of Mathematics and Center of Nonlinear Equations, China University of Mining and Technology, Xuzhou 221116, People's Republic of China sftian@cumt.edu.cn shoufu2006@126.com;3. Department of Mathematics and Center of Nonlinear Equations, China University of Mining and Technology, Xuzhou 221116, People's Republic of China |
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Abstract: | By using the extended Harrison and Estabrook's differential forms approach, in this paper, we investigate the Lie symmetries of the continuous and discrete dispersive long waves system, respectively. Based on this method, two closed ideals written in terms of a set of differential forms are constructed for the dispersive long waves systems. Furthermore, some invariant solutions are presented for such systems. By a direct computation, it is shown that the discrete dispersive long waves system admits a Kac-Moody-Virasoro type and a Virasoro-like type Lie algebra, respectively. Finally, we present an interesting relationship between the continuous case and a modified dispersive long waves system, which can be used to find nonlocal properties for such systems with each other. |
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Keywords: | Dispersive long waves system Lie symmetry Conservation law Nonlocally related systems Geometric approach Kac-Moody-Virasoro algebra |
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