摘要
Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.
Whitham–Broer–Kaup（WBK） equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.
作者
周伟
陆斌
Wei Zhou Bin Lu(School of Mathematical Sciences, Anhui University, Hefei 230601, China)
基金
Supported by the Key Foundation of Anhui Education Bureau under Grant No.KJ2013A028
the 211 Project of Anhhui University under Grant No.J18520104
Scientific Training Project for University Students
National Natural Science Foundation of China under Grant Nos.11471015,11571016
Natural Science Foundation of Anhui Province under Grant No.1408085MA02
