Lie symmetry analysis and reduction of a new integrable coupled KdV system
Lie symmetry analysis and reduction of a new integrable coupled KdV system
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DOI：
10.1088/1009-1963/16/2/006
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发表时间：
2007-02
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影响因子：
--
通讯作者：
Su-Ping Qian;Li-xin Tian
中科院分区：
文献类型：
--
作者：
Su-Ping Qian;Li-xin Tian
在本文中，研究了新的可积耦合 Korteweg-de Vries (KdV) 方程组的李对称性。使用方程组的一些对称子代数，我们获得了五种类型的显着相似性约简。由简化方程得到耦合KdV方程组的丰富解，如孤立波解、指数解、有理解和多项式解等。特别是，可以通过 Painlevé I 超越函数获得一类简化方程的群不变解。
In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg–de Vries (KdV) equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invariant solution of reduced equations can be acquired by means of the Painlevé I transcendent function.