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A new numerical method has been developed to propagate short wave equation pulses over indefinite distances.The method, Wave Confinement, utilizes a newly developed nonlinear partial differential equation that propagates basis function according to the wave equation.The discretized equation can be solved without any numerical dissipation.The method can also be used to solve for harmonic waves in the high frequency (Eikonal) limit, including multiple arrivals.The solution involves discretizing the wave equation on a uniform Eulerian grid and adding a simple nonlinear Confinement term.