# Self-acceleration in non-Hermitian Systems

## TL;DR

This paper explores the phenomenon of self-acceleration in non-Hermitian systems, revealing novel wave effects and the existence of integrable self-accelerating waves without the need for balanced gain and loss.

## Contribution

It demonstrates the existence of self-accelerating waves in non-Hermitian Hamiltonians, including constant intensity waves without balanced gain and loss, and uncovers unique effects in PT and non-PT symmetric systems.

## Key findings

- Self-accelerating waves exist in non-Hermitian Hamiltonians.
- Novel wave effects are unique to non-Hermitian systems.
- Self-accelerating constant intensity waves can occur without balanced gain and loss.

## Abstract

We study self-acceleration in PT and non-PT symmetric systems. We find some novel wave effects that appear uniquely in non-Hermitian systems. We show that integrable self-accelerating waves exist if the Hamiltonian is non-Hermitian. We find that self-accelerating constant intensity waves are possible even when gain and loss are not balanced in the system.