Abstract
Assuming a symmetric matrix-valued potential, we consider the associated θ-periodic Schrödinger operators Hθ on intervals [0,P], where in our applications P denotes the period of a stationary periodic solution to a nonlinear evolutionary PDE. We relate the Morse index of Hθ to certain Maslov indices, and apply our theory to operators obtained when Allen–Cahn equations and systems are linearized about stationary periodic solutions.
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