In this paper, a unified formula of a series of exact solutions for the coupled Schrödinger-KdV equation is obtained by using Hirota bilinear method and trial function method. These solutions contain bi-soliton solution, singular periodic amplitude solution and breather soliton solution. The results contribute to a better understanding of the structure of the solutions and non-linear phenomena for the coupled Schrödinger-KdV equation. Introduction Takao Yoshinaga et al. studied nonlinear

more »

... tion between long and short waves from the following model, which was called coupled Schrödinger-KdV equation [1] .