2017/02/23 by Jan Bouwe van den Berg, Berg, Jan Bouwe van den, Maxime Breden +5
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1702.07412
openalex publication_date 2017/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove existence of symmetric homoclinic orbits for the suspension bridge equation u""+βu" + eu-1=0 for all parameter values β∈ [0.5,1.9]. For each β, a parameterization of the stable manifold is computed and the symmetric homoclinic orbits are obtained by solving a projected boundary value problem using Chebyshev series. The proof is computer-assisted and combines the uniform contraction theorem and the radii polynomial approach, which provides an efficient means of determining a set, centered at a numerical approximation of a solution, on which a Newton-like operator is a contraction.