Travelling waves dynamics in a nonlinear parabolic equation with a shifted spatial argument

The local dynamics of a nonlinear parabolic equation on a circle with a shifted spatial argument and a small diffusion is studied. It is proved that the travelling waves interaction satisfies to 1:2 principle. The maximum principle for amplitudes with coefficient 2/3 is established. A number of stable travelling waves increases when the diffusion coeffcient tends to zero.