Fractal scattering of Gaussian solitons in directional couplers with logarithmic nonlinearities

TL;DR

This study investigates the complex fractal scattering behavior of Gaussian solitons in a nonlinear medium with logarithmic nonlinearity, revealing chaotic collision patterns and methods for controlling soliton interactions.

Contribution

It introduces a variational and numerical analysis of soliton collisions in a nonintegrable logarithmic nonlinear Schrödinger system, highlighting fractal scattering and control mechanisms.

Findings

Observation of fractal scattering patterns in soliton collisions

Identification of reflection/transmission windows within chaotic regions

Potential control of soliton scattering and bound state lifetimes

Abstract

In this paper we study the interaction of Gaussian solitons in a dispersive and nonlinear media with log-law nonlinearity. The model is described by the coupled logarithmic nonlinear Schr\"odinger equations, which is a nonintegrable system that allows the observation of a very rich scenario in the collision patterns. By employing a variational approach and direct numerical simulations, we observe a fractal-scattering phenomenon from the exit velocities of each soliton as a function of the input velocities. Furthermore, we introduce a linearization model to identify the position of the reflection/transmission window that emerges within the chaotic region. This enable us the possibility of controlling the scattering of solitons as well as the lifetime of bound states.