Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle (Q1880772)

The authors investigate scalar semilinear parabolic reaction-advection-diffusion equations with periodic boundary conditions in one space dimension. The translational invariance generates so-called rotating wave solutions which are periodic in space and time. The authors use zero number properties of the solutions to establish necessary and sufficient conditions for the existence of heteroclinic orbits, connecting rotating waves at time \(\pm\infty\). The results give a complete combinatorial description of the attractor of this parabolic equation under suitable dissipativity assumptions.