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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…
math.AP2009★ 27 cited
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…