Critical velocity in kink-defect interaction models: Rigorous results

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...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 269; no. 4; pp. 3282 - 3346
Main Authors Gomide, Otávio M.L., Guardia, Marcel, Seara, Tere M.
Format Journal Article
LanguageEnglish
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
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Summary: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 Hε is destroyed giving rise to heteroclinic connections between certain elements (at infinity) for exponentially small (in ε) energy levels. In this setting Melnikov theory does not apply because there are exponentially small phenomena.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2020.02.030