TY - JOUR

T1 - One- and two-dimensional solitary wave states in the nonlinear kramers equation with movement direction as a variable

AU - Sakaguchi, Hidetsugu

AU - Ishibashi, Kazuya

N1 - Publisher Copyright:
© 2018 The Physical Society of Japan.

PY - 2018

Y1 - 2018

N2 - 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 ϕ. We show that one-dimensional 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.

AB - 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 ϕ. We show that one-dimensional 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.

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U2 - 10.7566/JPSJ.87.064001

DO - 10.7566/JPSJ.87.064001

M3 - Article

AN - SCOPUS:85046907603

SN - 0031-9015

VL - 87

JO - journal of the physical society of japan

JF - journal of the physical society of japan

IS - 6

M1 - 064001-1

ER -