Asymptotic Theory and Slow Characteristics Solution Techniques for Weakly Non-linear Hyperbolic Partial Diierential Equations Asymptotic Theory and Slow Characteristics Solution Techniques for Weakly Non-linear Wave Equations on Semi-innnite Domains

We prove the existence and uniqueness of solutions of weakly non-linear wave equations in the region x > 0; t > 0 under arbitrary initial and boundary conditions. We also establish the asymptotic validity of formal perturbation approximations to the solutions. The asymptotics of these equations require two slow scales, one spatial, one temporal. We formulate a multiple-scale perturbation procedure, based on a set of scaled characteristic variables , which provides a simpliied description of the slow-scale interaction between forward and backward going wave components. We illustrate the procedure by applying it to a weakly nonlinear wave equation with a cubic nonlinearity.