Multiple-soliton and periodic solutions to space–time fractional Whitham–Broer–Kaup equations
State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China
2 College of Science, Inner Mongolia University of Technology, 010051, Hohhot, China
Accepted: 7 December 2021
Published online: 23 December 2021
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 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.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021