From decoupled integrable models to coupled ones via a deformation algorithm

Abstract

By using a reconstruction procedure of conservation laws of different models, the deformation algorithm proposed by Lou, Hao and Jia has been used to a new application such that a decoupled system becomes a coupled one. Using the new application to some decoupled systems such as the decoupled dispersionless Korteweg–de Vries (KdV) systems related to dispersionless waves, the decoupled KdV systems related to dispersion waves, the decoupled KdV and Burgers systems related to the linear dispersion and diffusion effects, and the decoupled KdV and Harry–Dym (HD) systems related to the linear and nonlinear dispersion effects, we have obtained various new types of higher dimensional integrable coupled systems. The new models can be used to describe the interactions among different nonlinear waves and/or different effects including the dispersionless waves (dispersionless KdV waves), the linear dispersion waves (KdV waves), the nonlinear dispersion waves (HD waves) and the diffusion effect. The method can be applied to couple all different separated integrable models.