Caustics of nonlinear waves |
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| Institution: | 1. School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, 430079, PR China;2. Department of Mathematics, The University of New England, Armidale, NSW 2351, Australia;1. Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany;2. Faculty of Maritime Sciences, Kobe University, Kobe 658-0022, Japan |
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| Abstract: | The behavior at caustics is analyzed for weakly nonlinear wave solutions of hyperbolic equations. It is shown that short waves, weak enough to be governed by linear or weakly nonlinear geometrical optics away from caustics, are governed by linear theory at and near caustics. For somewhat stronger waves, for which linear theory does not suffice at caustics, a weakly nonlinear caustic theory is developed. It leads to an equation derived by Guiraud, Hayes, and Seebass for gas dynamics. |
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