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arXiv · 1702.07412

Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof

Jan Bouwe van den Berg·Maxime Breden·Jean-Philippe Lessard·Maxime Murray
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Abstract

In this paper, we prove existence of symmetric homoclinic orbits for the suspension bridge equation $u""+\beta u" + e^u-1=0$ for all parameter values $\beta \in [0.5,1.9]$. For each $\beta$, 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.

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Jan Bouwe van den Berg, Maxime Breden, Jean-Philippe Lessard, Maxime Murray. 2017-02-23. Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof. https://arxiv.org/abs/1702.07412

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