One- and two-dimensional solitary wave states in the nonlinear kramers equation with movement direction as a variable

Hidetsugu Sakaguchi, Kazuya Ishibashi

Research output: Contribution to journalArticlepeer-review

Abstract

We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable Ø. We show that onedimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - Apr 13 2018

All Science Journal Classification (ASJC) codes

  • General

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