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Nonlinear dispersive or dissipative waves in inhomogeneous media. (English) Zbl 1230.35094
Summary: The singular perturbation method is applied to a class of nonlinear partial differential equations to reduce them into a single nonlinear equation presenting the wave propagation in an inhomogeneous medium. The coupling between nonlinear and dispersive or dissipative effects is shown to determine the order of the coordinate-stretching uniquely. The theory is applied to weak shock waves, shallow water waves and oblique magneto-acoustic waves.

MSC:
35Q35 PDEs in connection with fluid mechanics
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