The slowly passage through the resonances and wave packets with the different carriers

TL;DR

This paper analyzes how solutions to a perturbed nonlinear Klein-Gordon equation evolve through multiple resonances, leading to a sequence of wave packets with different oscillatory carriers, providing a detailed asymptotic description.

Contribution

It offers a comprehensive asymptotic analysis of wave packet formation during slow passage through multiple resonances in a nonlinear Klein-Gordon equation.

Findings

Sequence of wave packets with different carriers is generated during resonance passage.

Asymptotic formulas describe the evolution of solutions through resonances.

The process is characterized by a detailed asymptotic framework.

Abstract

Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The perturbation is represented by finite collections of harmonics. The frequencies of the perturbation vary slowly and pass through the resonant values consecutively. The resonances lead to the sequence of the wave packets with the different fast oscillated carriers. Full asymptotic description of this process is presented.