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

Abstract

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.

Keywords

• Multiple scale
• perturbation
• nonlinear
• waves.