中国物理B ›› 2007, Vol. 16 ›› Issue (2): 303-309.doi: 10.1088/1009-1963/16/2/006
钱素平1, 田立新2
Qian Su-Ping(钱素平)a)b)† and Tian Li-Xin(田立新)b)
摘要: 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 Painlev\'e I transcendent function.
中图分类号: (Lie algebras of Lie groups)