Many-body interaction in fast soliton collisions

TL;DR

This paper develops a reduced model to analyze multi-pulse interactions in fast soliton collisions under weak nonlinear loss, revealing that higher-order pulse interactions significantly influence amplitude shifts and collision dynamics.

Contribution

The study introduces a generalized reduced model for $n$-pulse interactions in NLS soliton collisions with weak nonlinear loss, highlighting the dominant role of multi-pulse effects.

Findings

Three-pulse interactions dominate amplitude shifts in four-soliton collisions.

Amplitude shifts depend strongly on initial soliton positions.

High-order $n$-pulse interactions are crucial in complex collision dynamics.

Abstract

We study $n$-pulse interaction in fast collisions of $N$ solitons of the cubic nonlinear Schr\"odinger (NLS) equation in the presence of generic weak nonlinear loss. We develop a reduced model that yields the contribution of $n$-pulse interaction to the amplitude shift for collisions in the presence of weak $(2m+1)$-order loss, for any $n$ and $m$. We first employ the reduced model and numerical solution of the perturbed NLS equation to analyze soliton collisions in the presence of septic loss $(m=3)$. Our calculations show that three-pulse interaction gives the dominant contribution to the collision-induced amplitude shift already in a full-overlap four-soliton collision, and that the amplitude shift strongly depends on the initial soliton positions. We then extend these results for a generic weak nonlinear loss of the form $G(|\psi|^{2})\psi$, where $\psi$ is the physical field and $G$ is a Taylor polynomial of degree $m_{c}$. Considering $m_{c}=3$, as an example, we show that three-pulse interaction gives the dominant contribution to the amplitude shift in a six-soliton collision, despite the presence of low-order loss. Our study quantitatively demonstrates that $n$-pulse interaction with high $n$ values plays a key role in fast collisions of NLS solitons in the presence of generic nonlinear loss. Moreover, the scalings of $n$-pulse interaction effects with $n$ and $m$ and the strong dependence on initial soliton positions lead to complex collision dynamics, which is very different from the one observed in fast NLS soliton collisions in the presence of cubic loss.