M. Chugunova and D. Pelinovsky

On quadratic eigenvalue problems arising in stability of discrete vortices

Linear Algebra and its Applications 431, 962-973 (2009)

We develop a count of unstable eigenvalues in a finite-dimensional quadratic eigenvalue problem arising in the context of stability of discrete vortices in a multi-dimensional discrete nonlinear Schrodinger equation. The count is based on the Pontryagin Invariant Subspace Theorem and the parameter continuation arguments. Another application of the method is given in the context of front–pulse solutions of neuron networks with piecewise constant nonlinear functions.

Quadratic eigenvalue problems, Pontryagin spaces, count of unstable eigenvalues, instability bifurcations, vortices in discrete nonlinear Schrodinger equations, front-pulse solutions in neuron networks.