Travelling waves in radially symmetric parabolic systems

Abstract

SynopsisIt is shown that all travelling or standing plane-wave solutions to certain radially symmetric parabolic systems may be found by solving a related scalar ordinary differential equation (ODE). The radially symmetric systems considered here are those whose reaction term is radially directed and points inward near infinity. The stability of these waves is also discussed. Many systems arising in the physical sciences are included in the class studied and so the classification and stability of the travelling waves has physical significance.