M. Chugunova and D. Pelinovsky
On quadratic eigenvalue problems arising in stability of discrete vortices
Linear Algebra and its Applications 431, 962-973 (2009)
Abstract:
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.
Keywords:
Quadratic eigenvalue problems, Pontryagin spaces, count of unstable eigenvalues, instability
bifurcations, vortices in discrete nonlinear Schrodinger equations, front-pulse solutions in
neuron networks.