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.

arXiv comment7 pages, 5 figures

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Cited by in corpus (2)

• Flip motion of solitary wave in an Ising-type Vicsek model
• One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable