Autoresonant soliton and decay pumping

TL;DR

This paper derives a primary resonance equation with external forcing, constructs a growing soliton solution, and identifies conditions for solution growth in dissipative media, advancing understanding of autoresonant phenomena.

Contribution

It introduces a new primary resonance equation with external force and provides conditions for soliton growth in dissipative systems.

Findings

Constructed a soliton with increasing amplitude over time.

Identified a necessary condition for solution growth in dissipative media.

Demonstrated the influence of decaying external force amplitude on soliton dynamics.

Abstract

The primary resonance equation in partial derivatives with external force and slowly varying frequency is derived. The leading-order term of asymptotic solution is constructed as a soliton with growing amplitude when time is large. This growing solution is obtained due to the decaying amplitude of the external force. A necessary condition for the growth of the solution in dissipative media is obtained also.