Electron. J. Diff. Eqns., Vol. 1998(1998), No. 03, pp. 1-10.

A scaled characteristics method for the asymptotic solution of weakly nonlinear wave equations

Chirakkal V. Easwaran

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.

Submitted August 5, 1997. Published January 31, 1998.
Math Subject Classification: 35C20, 35L20.
Key Words: Multiple scale, perturbation, nonlinear, waves.

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Chirakkal V. Easwaran
Department of Mathematics and Computer Science, State University of New York, New Paltz, NY 12561 USA
e-mail: easwaran@mcs.newpaltz.edu
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