Exact Solutions of the Coupled KdV system via a Formally Variable Separation Approach

Most of the nonlinear physics systems are essentially nonintegrable. There is no very good analytical approach to solve nonintegrable system. The variable separation approach is a powerful method in linear physics. In this letter, the formal variable separation approach is established to solve the generalized nonlinear mathematical physics equation. The method is valid not only for integrable models but also for nonintegrable models. Taking a nonintegrable coupled KdV equation system as a simple example, abundant solitary wave solutions and conoid wave solutions are revealed.