Critical velocity in kink-defect interaction models: rigorous results

• Published in: arXiv.org
• Main Authors: Gomide, Otávio M L, Guardia, Marcel, Seara, Tere M
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 08.11.2018
• Subjects: Critical velocity; Energy levels; Interaction models; Mathematics - Dynamical Systems
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1811.03699

In this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More specifically, we prove that a heteroclinic orbit in the energy level \(0\) of a \(2\)-dof Hamiltonian \(H_\epsilon\) is destroyed giving rise to heteroclinic connections between certain elements (at infinity) for exponentially small (in \(\epsilon\)) energy levels. In this setting Melnikov theory does not apply because there are exponentially small phenomena.