We review evolutionary models on quantum graphs expressed by linear and nonlinear
partial differential equations. Existence and stability of the standing waves trapped on …

We consider the sine-Gordon equation on metric graphs with simple topologies and derive
vertex boundary conditions from the fundamental conservation laws together with …

We consider quantum graphs with transparent branching points. To design such networks,
the concept of transparent boundary conditions is applied to the derivation of the vertex …

We elaborate a theoretical description of large Josephson junctions which is based on
Werthamer's microscopic tunneling theory. The model naturally incorporates coupling of …

We consider the nonlinear Schrödinger (NLS) equation with the subcritical power
nonlinearity on a star graph consisting of N edges and a single vertex under generalized …

We study dynamics of Dirac solitons in prototypical networks modeling them by the
nonlinear Dirac equation on metric graphs. Stationary soliton solutions of the nonlinear …

We consider the reflectionless transport of solitons in networks. The system is modeled in
terms of the nonlinear Schrödinger equation on metric graphs, for which transparent …

We consider the stationary sine-Gordon equation on metric graphs with simple topologies.
Exact analytical solutions are obtained for different vertex boundary conditions. It is shown …

In this paper, the finite point method is discussed for solving the initial‐boundary value
problem associated with the sine‐Gordon equation in two‐dimensional domains arising in …

In the present study the interaction of a sine-Gordon kink with a localized inhomogeneity is
considered. In the absence of dissipation, the inhomogeneity considered is found to impose …