Asymptotic investigation of a nonlinear model of string vibrations

Abstract

The mathematical model of nonlinear oscillations of a weightless string is analysed. The uniformly valid asymptotic approximation in the long time interval, which is inversely proportional to the small parameter, is constructed. This asymptotic approximation is a solution of averaged along characteristics integro-differential system. A method for constructing special approximations of its solutions is proposed.

Keywords

• resonance
• asymptotic methods
• nonlinear waves
• averaging