Boris Buffoni, EPFL
The 6-dimensional system
A´´´´ &= A ( 1 – A^2 – g B^2 )\\
B´´ & = e^2 B ( -1 + g A^2 + B^2 )
appears in an approximation of the classical Bénard-Rayleigh problem near the convective instability threshold, where \(e>0\) and \(g>1\) are two parameters.
Heteroclinic orbits from \((A,B)=(1,0)\) to \((0,1)\) correspond to configurations in which two families of convective rolls with orthogonal orientations coexist (“orthogonal walls”).
The derivation of the system will be briefly described and heteroclicinic orbits obtained by a variational method.
Two limiting cases will be considered more carefully: \(e>0\) small and \(g-1>0\) small.
This is joint work with M. Haragus and G. Iooss.