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

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.

7 pages, 5 figures

References in corpus (2)

• Novel type of phase transition in a system of self-driven particles
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis

Cited by in corpus (1)

• Flip motion of solitary wave in an Ising-type Vicsek model