Научный архив: статьи

Two-dimensional waveguides coupled through small windows are considered. First terms of the asymptotic expansion of resonances are obtained and studied for the case when the distance between the windows decreases. Method of matching of the asymptotic expansions of solutions of boundary value problems is used.

We study quantum graphs with the Dirac operator on edges and the Kirchhoff coupling condition at the vertices. The number of resonances is determined numerically. It is revealed how the parameters of the quantum graph (particularly, the topological structure and the volume of the quantum graph as well as the parameters of the Dirac operator) affect the number of resonances.