Asymptotic method for approximation of resonant interaction of nonlinear multidimensional hyperbolic waves

Abstract

A method of averaging along characteristics of weakly nonlinear hyperbolic systems, which was presented in earlier works of the author for one dimensional waves, is generalized for some cases of multidimensional wave problems. In this work we consider such systems and discuss a way to use the internal averaging along characteristics for new problems of asymptotical integration.

Key words:

• perturbation methods
• averaging
• nonlinear hyperbolic equations
• waves’ interaction
• resonances