5 papers
Transparent Boundary Conditions for the Heat Equation on Metric Graphs
Jasur Matrasulov, Jambul Yusupov, Matthias Ehrhardt
We study transparent boundary conditions (TBCs) for the time-dependent heat equation in a branching, quasi-one-dimensional domain modeled as a metric star graph. By combining the c…
Transparent boundary conditions for the spatially discrete Schrödinger equation: Reflectionless quantum transport in 1D lattices
Mashrab E. Akramov, Jambul R. Yusupov, Matthias Ehrhardt +1
We construct exact transparent boundary conditions (TBCs) for a time-continuous, spatially discrete Schrödinger equation that models a one-dimensional quantum lattice. Using a rece…
Kink-antikink soliton solutions of the nonlinear Klein-Gordon equation on branched structures
Q. U. Asadov, K. K. Sabirov, J. R. Yusupov
In this paper, we investigate the nonlinear Klein-Gordon equation on a metric star graph with three semi-infinite bonds. At the branching point, we impose a weighted continuity con…
Discrete Schrodinger equation on graphs: An effective model for branched quantum lattice
M. Akramov, C. Trunk, J. Yusupov +1
We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solu…
Transparent boundary conditions for the stationary Schroedinger equation via Weyl-Titchmarsh theory
V. A. Derkach, C. Trunk, J. R. Yusupov +1
We propose a general approach for deriving transparent boundary conditions for the stationary Schroedinger equation with arbitrary potential. It is proven that the transparent boun…