Critical velocity in kink-defect interaction models: Rigorous results

• Published in: Journal of Differential Equations Vol. 269; no. 4; pp. 3282 - 3346
• Main Authors: Gomide, Otávio M.L., Guardia, Marcel, Seara, Tere M.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 05.08.2020
• Subjects: Critical velocity; Exponentially small phenomena; Hamiltonian systems; Heteroclinic connections; Kink; Sine-Gordon equation; Kink; Hamiltonian systems; Exponentially small phenomena; Sine-Gordon equation; Critical velocity; Heteroclinic connections

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 H...