Multiple-soliton and Periodic Solutions to Space-time Fractional Whitham-Broer-Kaup Equations

In this paper, the space-time fractional Whitham-Broer-Kaup equations are investigated. By means of new fractional scaling transformations, the fractional nonlinear system of different time and space orders is transformed to the integer one. The multiple solitary solutions and periodic solutions are obtained respectively. All those solutions are given exactly by introducing new scaling transformations, which makes our study is unique and different from most existing studies. It is expected that exact solutions for nonlinear wave system of fractional order can be handled in the similar way.