Derivatives of the Evans function and (modified) Fredholm determinants for first order systems

DOI10.1002/mana.201000074zbMath1225.47131OpenAlexW2022441191MaRDI QIDQ3092754

Yuri Latushkin, Mita Das

Publication date: 11 October 2011

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201000074

zbMATH Keywords

Schrödinger operatorsJost functionsEvans functionsstability of traveling wavesinfinite determinants

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) General spectral theory of ordinary differential operators (34L05) Perturbation theory of linear operators (47A55) Linear ordinary differential equations and systems (34A30) Schrödinger operator, Schrödinger equation (35J10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Applications of operator theory to differential and integral equations (47N20)

Related Items (4)

Stable foliations near a traveling front for reaction diffusion systems ⋮ Finding eigenvalues of holomorphic Fredholm operator pencils using boundary value problems and contour integrals ⋮ Stability of a Planar Front in a Class of Reaction-Diffusion Systems ⋮ The infinite dimensional Evans function

Cites Work

• Nonselfadjoint operators, infinite determinants, and some applications
• Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves
• Asymptotic stability of solitary waves
• Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
• Absolute and convective instabilities of waves on unbounded and large bounded domains
• Eigenvalues and resonances using the Evans function
• Evans function and blow-up methods in critical eigenvalue problems
• Evans functions, Jost functions, and Fredholm determinants
• Analytic perturbation of operators in Banach spaces
• The Evans Function and Generalized Melnikov Integrals
• Eigenvalues, and instabilities of solitary waves
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