In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...

We propose an algorithm for an asymptotic model of shallow-water wave dynamics in a periodic domain. The algorithm is based on the Hamiltonian structure of the equation and corresponds to a completely integrable particle lattice. In particular, “periodic particles” are introduced in the algorithm for waves travelling through the domain. Each periodic particle in this method travels along a char...

A 2D Large Time Step (LTS) explicit scheme on structured grids is presented in this work. It is first detailed and analysed for the 2D linear advection equation and then applied to the 2D shallow water equations. The dimensional splitting technique allows us to extend the ideas developed in the 1D case related to source terms, boundary conditions and the reduction of the time step in the presen...