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Using a variational method, we prove the existence of heteroclinic solutionsfor a 6dimensional system of ordinary differential equations. We derive thissystem from the classical B{\'e}nard-Rayleigh problem near the convectiveinstability threshold. The constructed heteroclinic solutions provide firstorder approximations for domain walls between two orthogonal convective rolls.

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