2021/04/20 by Pava, Jaime Angulo, Plaza, Ramón G. · 1 citation
#35J61 #35Q51 #35Q53 #47E05 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2104.09911
The aim of this work is to establish a 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 δ'-interaction type, it is shown that these kink-soliton type stationary profiles 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 H1(Y)× L2(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.