Solitary Wave Propagation of the Generalized Rosenau-Kawahara-RLW Equation in Shallow Water Theory with Surface Tension

This paper addresses a numerical approach for computing the solitary wave solutions of the generalized Rosenau-Kawahara-RLW model established by coupling the generalized Rosenau-Kawahara and Rosenau-RLW equations. The solution of this model is accomplished by using the finite difference approach and the upwind local radial basis functions-finite difference. Firstly, the PDE is transformed into a nonlinear ODEs system by means of the radial kernels. Secondly, a high-order ODE solver is implemented for discretizing the system of nonlinear ODEs. The main advantage of this technique is its lack of need for linearization. The global collocation techniques impose a significant computational cost, which arises from calculating the dense system of algebraic equations. The proposed technique estimates differential operators on every stencil. As a result, it produces sparse differentiation matrices and reduces the computational burden. Numerical experiments indicate that the method is precise and efficient for long-time simulation.

Automated summary

This paper proposes a numerical approach for computing the solitary wave solutions of the generalized Rosenau-Kawahara-RLW model. The approach transforms the PDE into a nonlinear ODEs system using radial kernels and discretizes the system using a high-order ODE solver. It reduces the computational burden and produces precise and efficient results.