Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation

DOI10.3934/DCDSB.2018097zbMath1406.35391OpenAlexW2789556784MaRDI QIDQ1756984

Milena Stanislavova, Aslihan Demirkaya

Publication date: 28 December 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018097

zbMATH Keywords

traveling wavesnonlinear beam equationorbital stabilityspectral stabilitystanding waves

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Stability in context of PDEs (35B35) Variational methods applied to PDEs (35A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Canonical models for contractions and nonselfadjoint linear operators (47A45) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Higher-order elliptic equations (35J30) PDEs in connection with mechanics of deformable solids (35Q74) Traveling wave solutions (35C07)

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Cites Work

• Orbital stability for periodic standing waves of the Klein-Gordon-Zakharov system and the beam equation
• The existence of ground states for fourth-order wave equations
• Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations
• Stability and instability of fourth-order solitary waves
• Solitary waves in nonlinear beam equations: Stability, fission and fusion
• Orbital stability of solitary waves for the Klein-Gordon-Zakharov equations
• Spectral stability analysis for special solutions of second order in time PDEs: the higher-dimensional case
• Linear stability analysis for travelling waves of second order in time PDE's
• Travelling Waves in a Suspension Bridge

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