New Lax pairs and Darboux transformation and its application to a shallow water wave model of generalized KdV type (Q460104)

Summary: New Lax pairs of a shallow water wave model of generalized KdV equation type are presented. According to this Lax pair, we constructed a new spectral problem. By using this spectral problem, we constructed Darboux transformation with the help of a gauge transformation. Applying this Darboux transformation, some new exact solutions including double-soliton solution of the shallow water wave model of generalized KdV equation type are obtained. In order to visually show dynamical behaviors of these double soliton solutions, we plot graphs of profiles of them and discuss their dynamical properties.