Unstable simple modes of the nonlinear string

DOI10.1090/qam/1388017zbMath0866.34044OpenAlexW2414265249MaRDI QIDQ4888064

Fred B. Weissler, Thierry Cazenave

Publication date: 14 July 1997

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/qam/1388017

zbMATH Keywords

Hamiltonian systemnonlinear vibrating string equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Second-order nonlinear hyperbolic equations (35L70) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Asymptotic properties of solutions to ordinary differential equations (34D05) Strings (74K05)

Related Items (16)

Unstable simple modes for a class of Kirchhoff equations ⋮ An instability result in the theory of suspension bridges ⋮ On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate ⋮ Instability of modes in a partially hinged rectangular plate ⋮ An Instability Result for Suspension Bridges ⋮ Beams with an intermediate pier: spectral properties, asymmetry and stability ⋮ Asymptotic finite-dimensional approximations for a class of extensible elastic systems ⋮ Energy transfer between modes in a nonlinear beam equation ⋮ Loss of energy concentration in nonlinear evolution beam equations ⋮ Transfer of energy from flexural to torsional modes for the fish-bone suspension bridge model ⋮ Resonance tongues for the Hill equation with Duffing coefficients and instabilities in a nonlinear beam equation ⋮ Instability results for a Hill equation coupled with an asymmetrically nonlinear oscillator ⋮ A road map to the blow-up for a Kirchhoff equation with external force ⋮ Torsional instability in suspension bridges: the Tacoma Narrows Bridge case ⋮ Which Residual Mode Captures the Energy of the Dominating Mode in Second Order Hamiltonian Systems? ⋮ On the instability tongues of the Hill equation coupled with a conservative nonlinear oscillator

This page was built for publication: Unstable simple modes of the nonlinear string