Critical velocity in kink-defect interaction models: Rigorous results

Author(s)

Gomide, Otavio M. L. ^{[1, 2]} ; Guardia, Marcel ^[3] ; Seara, Tere M. ^[3]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Dept Math, BR-13083970 Campinas, SP - Brazil

^[2] Univ Fed Goias, IME, Dept Math, BR-74690900 Goiania, Go - Brazil

^[3] Univ Politecn Cataluna, Dept Matemat Aplicada 1, Diagonal 647, Barcelona 08028 - Spain

• Document type: Journal article
• Source: Journal of Differential Equations; v. 269, n. 4, p. 3282-3346, AUG 5 2020.
• Web of Science Citations: 0

Abstract

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. (C) 2020 The Author(s). Published by Elsevier Inc. (AU)

• FAPESP's process: 15/22762-5 - Structural Stability of Nonsmooth Systems on Tridimensional Manifolds
• Grantee: Otávio Marçal Leandro Gomide
• Support Opportunities: Scholarships in Brazil - Doctorate