We introduce and examine an algorithm for an asymptotic model of wave propagation in shallow-water. The algorithm is based on the Hamiltonian structure of the nonlinear equation, and corresponds to a completely integrable particle lattice. Each "particle" in this method travels along a characteristic curve of the shallow water equation. The resulting system of nonlinear ordinary differential equations can have solutions that blow-up in finite time. We isolate the conditions for global existence

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... and follow up with an l 1 -norm estimate that establishes convergence of the method in the limit of zero spatial step size and infinite number of particles. A fast summation algorithm is introduced to evaluate the integrals of the particle method so that the computational cost is reduced from O(N 2 ) to O(N ), where N is the number of particles. Finally we include results on the study of the nonlinear equation posed in the quarter (spacetime) plane. We discuss the minimum number of boundary conditions required for solution uniqueness and the complete integrability in this case. A modified particle scheme illustrates this with numerical examples.