A Scaled Characteristics Method for the Asymptotic Solution of Weakly Nonlinear Wave Equations
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We formulate a multi-scale perturbation technique to asymptotically solve weakly nonlinear hyperbolic equations. The method is based on a set of scaled characteristic coordinates. We show that this technique leads to a simplified system of ordinary differential equations describing the weakly nonlinear interaction between left and right running waves. Using this method, a uniformly valid first order solution of a prototype nonlinear equation is derived.
CitationEaswaran, C. V. (1998). A scaled characteristics method for the asymptotic solution of weakly nonlinear wave equations. Electronic Journal of Differential Equations, 1998(03), pp. 1-10.
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