Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

Abstract

Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{é}nard-Rayleigh problem near the convective instability threshold. The constructed heteroclinic solutions provide first order approximations for domain walls between two orthogonal convective rolls.