Spectral analysis of \(\theta\)-periodic Schrödinger operators and applications to periodic waves (Q1678257)

The authors consider a Sturm-Liouville operator with a continuous symmetric matrix-valued potential on a compact interval with periodic boundary conditions. With this operator they associate a one-parameter family of a pair of Lagrangian subspaces (too complicated to specify in a brief review) the Maslov index of which is studied. In four sections the general theory of this index is tailored to suit the particular application they have in mind, viz., the Allen-Cahn equation (and systems of equations), linearised about a stationary periodic solution. The corresponding two examples are numerically analysed in the final section.