Instability theory of kink and anti-kink profiles for the sine-Gordon equation on Josephson tricrystal boundaries

[摘要] The aim of this work is to establish an instability study for stationary kink and antikink/kink profiles solutions for the sine-Gordon equation on a metric graph with a structure represented by a Y-junction so-called a Josephson tricrystal junction. By considering boundary conditions at the graph-vertex of delta'-interaction type, it is shown that kink profiles which are continuous at the vertex, as well as anti-kink/kink profiles possibly discontinuous at the vertex, are linearly (and nonlinearly) unstable. The extension theory of symmetric operators, Sturm-Liouville oscillation results and analytic perturbation theory of operators are fundamental ingredients in the stability analysis. The local well-posedness of the sine-Gordon model in H-1(Y) x L-2(Y) is also established. The theory developed in this investigation has prospects for the study of the (in)-stability of stationary wave solutions of other configurations for kink-solitons profiles. (C) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-12-01

[关键词] sine-Gordon model;Josephson tricrystal junction;Kink;Anti-kink solitons;Extension theory;Instability