Easwaran, Chirakkal V.
A scaled characteristics method for the asymptotic solution of weakly nonlinear wave equations
Electron. J. Differ. Equ. 1998, Paper 3, 10 p. (1998)
Summary: 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.
Mathematics Subject Classification
multiple scale, perturbation, nonlinear, waves