Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
By Todd Kapitula, Panayotis G. Kevrekidis, Bjorn Sandstede. 2004
201 citations recorded by the source corpus.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/5881a9423de18329a1ad2bd138d3c3722e0b2f5f
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In Mathematical Physics
- C. Zeng
- Zhiwu Lin
- Dmitry E. Pelinovsky
- Marina Chugunova
- Dimitri J. Frantzeskakis
- V. Vougalter
- Todd Kapitula
- Mariana Haˇraˇguş
In Statistical and Nonlinear Physics
- C. Zeng
- Zhiwu Lin
- Dmitry E. Pelinovsky
- Marina Chugunova
- Dimitri J. Frantzeskakis
- V. Vougalter
- Todd Kapitula
- Mariana Haˇraˇguş
Citations in the corpus
- Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs (2017, background): “In most of these papers, J is assumed to have a bounded inverse ([18] [21] [44] [47]), or J |(ker J) has a bounded inverse, as in the cases of periodic”
- Stability of discrete solitons in nonlinear Schrödinger lattices (2005, methodology): “It was recently studied [40, 41] that there exists a closure relation between the negative index of the linearized Hamiltonian H and the number of unstable eigenvalues of the linearized operator JH.”
- An Instability Index Theory for Quadratic Pencils and Applications (2012, background): “, see [18,25,26,32] and the references therein), and for this problem it has firmly been established that the intuition is indeed correct.”
- Spectra of positive and negative energies in the linearized NLS problem (2005, methodology): “This part of the spectrum produces instabilities of the excited states, in which case the linearized NLS problem (1.2) has eigenvalues z with Im(z )> 0. Sharp bounds on the number and type of unstable eigenvalues of the linearized operator L are given in terms of negative eigenvalues of the energy o”
- Count of eigenvalues in the generalized eigenvalue problem (2006, methodology): “The closure relation (6.12) was also discussed in [ KKS04 ] in a more general context.”
- On the spectra of periodic waves for infinite-dimensional Hamiltonian systems (2008, methodology): “In particular, if Im(JγLγ) = 0, we recover the results presented in [18, 19], although the proof is different.”