Spectral analysis of \(\theta\)-periodic Schrödinger operators and applications to periodic waves
type: Item
instance of: scholarly article
title: Spectral analysis of \(\theta\)-periodic Schrödinger operators and applications to periodic waves
zbMATH Open document ID: 1385.53073
author: Peter Howard
author: Soyeun Jung
published in: Journal of Differential Equations
publication date: 2017-11-14T00:00:00Z
review text: The authors consider a Sturm-Liouville operator with a continuous symmetric matrix-valued potential on a compact interval with periodic boundary conditions. With this operator they associate a one-parameter family of a pair of Lagrangian subspaces (too complicated to specify in a brief review) the Maslov index of which is studied. In four sections the general theory of this index is tailored to suit the particular application they have in mind, viz., the Allen-Cahn equation (and systems of equations), linearised about a stationary periodic solution. The corresponding two examples are numerically analysed in the final section.
reviewed by: Hubert Kalf
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35K91
zbMATH DE Number: 6806996
MaRDI profile type: Publication
full work available at URL: j.jde.2017.10.018
OpenAlex ID: W2767552149
cites work: The Maslov index: A functional analytical definition and the spectral flow formula
cites work: On the maslov index
cites work: Fredholm-Lagrangian-Grassmannian and the Maslov index
cites work: Spectral analysis of stationary solutions of the Cahn-Hilliard equation
cites work: Spectral analysis for periodic solutions of the Cahn-Hilliard equation on \(\mathbb R\)
cites work: The Maslov index and spectral counts for linear Hamiltonian systems on \([0, 1]\)
cites work: The Maslov index for Lagrangian pairs on \(\mathbb{R}^{2 n}\)
cites work: The Maslov and Morse indices for Schrödinger operators on \([0,1]\)
cites work: Pointwise asymptotic behavior of modulated periodic reaction-diffusion waves
cites work: The Morse and Maslov indices for matrix Hill's equations
cites work: Counting spectrum via the Maslov index for one dimensional \(\theta\)-periodic Schrödinger operators
cites work: Pointwise nonlinear stability of nonlocalized modulated periodic reaction-diffusion waves
cites work: An overview of periodic elliptic operators
cites work: Self-Adjoint Fredholm Operators And Spectral Flow
cites work: The Maslov index for paths
cites work: Q3873024
DOI: 10.1016/J.JDE.2017.10.018
description: scientific article; zbMATH DE number 6806996