Kaup-Boussinesq方程的留数对称和相互作用解

Residual Symmetries and Interaction Solutionsof the Kaup-Boussinesq Equations

研究了Kaup-Boussinesq(KB)方程的留数对称和相互作用解.首先,通过Painlevé截断展开得到KB方程的留数对称,并将其留数对称局域化;其次,运用相容Riccati展开法,证明了该方程是相容Riccati展开可解的;最后,通过求解相容性方程,并且借助雅可比椭圆函数构造了孤立波与椭圆周期波的相互作用解.

In this paper,the residual symmetry and interaction solution of the Kaup-Boussinesq equations are studied.First,the truncated Painlevémethod is developed to obtain the residual symmetry of the Kaup-Boussinesq equations.Then,the Kaup-Boussinesq equations are proved to be consistent Riccati expansion(CRE)solvable.Finally,with the help of the Jacobian elliptic functions,the interaction solutions of solitary wave and elliptic periodic wave are obtained through solving the consistency equation.