58 citations · 161 across the 9 of their papers we have counts for
9 papers
A reformulated Krein matrix for star-even polynomial operators with applications
Todd Kapitula, Ross Parker, Björn Sandstede
In its original formulation the Krein matrix was used to locate the spectrum of first-order star-even polynomial operators where both operator coefficients are nonsingular. Such op…
Existence, Stability and Dynamics of Harmonically Trapped One-Dimensional Multi-Component Solitary Waves: The Near-Linear Limit
Haitao Xu, Panayotis G. Kevrekidis, Todd Kapitula
In the present work, we consider a variety of two-component, one-dimensional states in nonlinear Schrodinger equations in the presence of a parabolic trap, inspired by the atomic p…
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…
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…
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…
An index theorem for the stability of periodic traveling waves of KdV type
Jared C. Bronski, Mathew A. Johnson, Todd Kapitula
We consider periodic solutions to equations of Korteweg-Devries type. While the stability theory for periodic waves has received much some attention the theory is much less develop…