Envelope quasi-solitons in dissipative systems with cross-diffusion

TL;DR

This paper introduces a new type of envelope quasi-solitons in reaction-cross-diffusion systems, exhibiting oscillatory behavior with a smooth envelope, similar to envelope solitons in the Nonlinear Schrödinger equation.

Contribution

It demonstrates the existence of envelope quasi-solitons with distinct velocities for oscillations and envelopes in dissipative reaction-cross-diffusion systems.

Findings

Identification of envelope quasi-solitons with oscillatory behavior

Distinct velocities for oscillations and envelopes

Comparison to envelope solitons in nonlinear Schrödinger equation

Abstract

We consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasi-soliton" pulses, which have fixed stable structure but can reflect from boundaries and penetrate each other. Presently we demonstrate a different type of quasi-solitons, with a phenomenology resembling that of the envelope solitons in Nonlinear Schroedinger equation: spatiotemporal oscillations with a smooth envelope, with the velocity of the oscillations different from the velocity of the envelope.