Wave Propagation and Resonance in a One-Dimensional Nonlinear Discrete Periodic Medium

DOI10.1137/S0036139998340315zbMath0937.37058OpenAlexW1976178335MaRDI QIDQ4943898

Anna Georgieva, Stephanos Venakides, Thomas Kriecherbauer

Publication date: 19 March 2000

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036139998340315

zbMATH Keywords

wave propagationsymmetriesdispersion relationtraveling wavesLyapunov-Schmidt methodFourier seriesbifurcation theorynonlinear dispersion relationparticle chainsnonlinear infinite diatomic chainnonresonant wave-numbersphotonic band-gap materials

Mathematics Subject Classification ID

Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems (37L50) Symmetries of infinite-dimensional dissipative dynamical systems (37L20)

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Existence and multiplicity of wave trains in a 2D diatomic face-centered lattice ⋮ Nonlinear Maxwell equations in inhomogeneous media ⋮ Modulation of uniform motion in diatomic Frenkel-Kontorova model ⋮ Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential ⋮ Discrete Modeling of Oscillatory Processes in a Blocky Medium

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