Solitary wave state in the nonlinear Kramers equation for self-propelled particles

TL;DR

This paper investigates the emergence and properties of solitary wave states in a system of self-propelled particles modeled by the nonlinear Kramers equation, revealing phase transition behaviors and wave interactions.

Contribution

It introduces a self-consistent method to approximate solitary wave solutions and characterizes the phase transition nature in the system.

Findings

Solitary wave states emerge from instability of uniform ordered states.

Two solitary waves can merge into a larger wave.

Phase transition to solitary wave state can be first or second order.

Abstract

We study collective phenomena of self-propagating particles using the nonlinear Kramers equation. A solitary wave state appears from an instability of the spatially uniform ordered state with nonzero average velocity. Two solitary waves with different heights merge into a larger solitary wave. An approximate solution of the solitary wave is constructed using a self-consistent method. The phase transition to the solitary wave state is either first-order or second-order, depending on the control parameters.