Oscillatory and Localized Perturbations of Periodic Structures and the Bifurcation of Defect Modes

DOI10.1137/140980302zbMath1334.34184arXiv1407.8403OpenAlexW2949634304MaRDI QIDQ3195478

Iva Vukićević, Vincent Duchêne, Michael I. Weinstein

Publication date: 19 October 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.8403

zbMATH Keywords

spectral gapdefect modesedge bifurcationsperiodic Schrodinger operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Bifurcation theory for ordinary differential equations (34C23) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (2)

Subwavelength Localized Modes for Acoustic Waves in Bubbly Crystals with a Defect ⋮ Defect Resonances of Truncated Crystal Structures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some singular perturbations of periodic operators
• The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential
• On the existence of eigenvalues of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H)
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Localized classical waves created by defects
• Homogenized description of defect modes in periodic structures with localized defects
• Scattering, Homogenization, and Interface Effects for Oscillatory Potentials with Strong Singularities
• Counting Defect Modes in Periodic Eigenvalue Problems
• Defect Modes and Homogenization of Periodic Schrödinger Operators
• A Short Proof of Zheludev's Theorem
• Midgap Defect Modes in Dielectric and Acoustic Media
• On the spectrum of a two-dimensional periodic operator with a small localized perturbation
• The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis
• On the spectrum of a periodic operator with a small localized perturbation
• Scattering and Localization Properties of Highly Oscillatory Potentials

This page was built for publication: Oscillatory and Localized Perturbations of Periodic Structures and the Bifurcation of Defect Modes