Transparent nonlinear networks

Nonlocal nonlinear Schrödinger equation on metric graphs: A model for generation and transport of parity-time-symmetric nonlocal solitons in networks

We consider the parity-time (PT)-symmetric, nonlocal, nonlinear Schrödinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. Soliton solutions are obtained for the simplest graph topologies, such as star and tree graphs. The integrability of the problem is shown by proving the existence of an infinite number of conservation laws. A model for soliton generation in such PT-symmetric optical fibers and their networks governed by the nonlocal nonlinear Schrödinger equation is proposed. Exact formulas for the number of generated solitons are derived for the cases when the problem is integrable. Numerical solutions are obtained for the case when integrability is broken.

Reflectionless propagation of Manakov solitons on a line: A model based on the concept of transparent boundary conditions

We consider the problem of the absence of backscattering in the transport of Manakov solitons on a line. The concept of transparent boundary conditions is used for modeling the reflectionless propagation of Manakov vector solitons in a one-dimensional domain. Artificial boundary conditions that ensure the absence of backscattering are derived and their numerical implementation is demonstrated.

Dirac particles in transparent quantum graphs: Tunable transport of relativistic quasiparticles in branched structures

We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the Dirac equation on metric graphs. Within such an approach, we derive simple constraints, which turn the usual Kirchhoff-type boundary conditions at the vertex equivalent to the transparent ones. Our method is applied to quantum star graph. An extension to more complicated graph topologies is straightforward.