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Abstract
Boussinesq-type nonlinear wave equations with dispersive terms are solved via split-step Fourier methods. We decompose the equations into linear and nonlinear parts, then solve them orderly. The linear part can be projected into phase space by a Fourier transformation, and resulting in a variable separable ordinary differential system, which can be integrated exactly. Next, by an invert Fourier transformation, the classical explicit fourth-order Runge–Kutta method is adopted to solve the nonlinear subproblem. To examine the numerical accuracy and efficiency of the method, we compare the numerical solutions with exact solitary wave solutions. Additionally, various initial-value problems for all the listed Boussinesq-type system are studied numerically. In the study, we can observe that sech 2-type waves for KdV-BBM system will split into several solitons, which is a very interesting physical phenomenon. The interaction between solitons, including overtaking and head-on collisions, is also simulated.
Acknowledgements
This work was supported by the Doctor Foundation of Jiangxi Normal University (no. 2057), the 2008 Young Growth Foundation of Jiangxi Normal University, the 2008 natural science foundation of Jiangxi Province, and State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences. The authors thank Dr Zhenli Xu for his zealous help and useful suggestions. The authors are grateful to the referees for their valuable comments and suggestions.