27 citations · 47 across the 4 of their papers we have counts for
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math-ph2012★ 1 cited
The Krein Matrix: General Theory and Concrete Applications in Atomic Bose-Einstein Condensates
Todd Kapitula, Panayotis Kevrekidis, Dong Yan
When finding the nonzero eigenvalues for Hamiltonian eigenvalue problems it is especially important to locate not only the unstable eigenvalues (i.e., those with positive real part…
math.AP2012★ 16 cited
A Hamiltonian-Krein (instability) index theory for KdV-like eigenvalue problems
Todd Kapitula, Atanas Stefanov
The Hamiltonian-Krein (instability) index is concerned with determining the number of eigenvalues with positive real part for the Hamiltonian eigenvalue problem , where…
math.AP2012★ 3 cited
An Instability Index Theory for Quadratic Pencils and Applications
Jared Bronski, Mathew A. Johnson, Todd Kapitula
Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic ope…