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 vari able separation approach is a powerful method in linear physics. In this le tter, the formal variable separation approach is established to solve the g eneralized nonlinear mathematical physics equation. The method is valid not only for integrable models but also for nonintegrable models. Taking a non integrable coupled KdV equation system as a simple example, abundant solita ry wave solutions and conoid wave solutions are revealed.