# Nonlinear interactions between solitons and dispersive shocks in focusing media

## TL;DR

This paper investigates how solitons interact with dispersive shocks in focusing media using the nonlinear Schrödinger equation, revealing that solitons pass through shocks with altered properties and sometimes become trapped, with analytical and numerical validation.

## Contribution

It provides a detailed analytical and numerical analysis of soliton-shock interactions in focusing media, highlighting new behaviors such as property changes and trapping.

## Key findings

- Solitons pass through shocks without radiation, with altered properties.
- Solitons can become trapped inside shock structures depending on initial velocity.
- Analytical predictions match numerical simulations.

## Abstract

Nonlinear interactions in focusing media between traveling solitons and the dispersive shocks produced by an initial discontinuity are studied using the one-dimensional nonlinear Schrodinger equation. It is shown that, when solitons travel from a region with nonzero background towards a region with zero background, they always pass through the shock structure without generating dispersive radiation. However, their properties (such as amplitude, velocity and shape) change in the process. A similar effect arises when solitons travel from a region with zero background towards a region with nonzero background, except that, depending on its initial velocity, in this case the soliton may remain trapped inside the shock-like structure indefinitely. In all cases, the new soliton properties can be determined analytically. The results are validated by comparison with numerical simulations.