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van den Berg, Jan Bouwe; Breden, Maxime; Lessard, Jean-Philippe; Murray, Maxime
Journal of Differential Equations, 03/2018, Letnik: 264, Številka: 5Journal Article
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.
