A completely integrable particle method for a nonlinear shallow-water wave equation in periodic domains

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 characteristic curve of the shallowwater wave model, determined by solving a system of nonlinear integral-differential equations. Accuracy tests for assessing the global properties of the method are performed and compared to more standard PDE algorithms.