Transparent nonlinear networks

Abstract

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 boundary conditions at the branching points are imposed. This allows to derive simple constraints, which link equivalent usual Kirchhoff-type vertex conditions to the transparent ones. Our approach is applied to a metric star graph. An extension to more complicated graph topologies is straight forward.

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Cited by in corpus (8)

• Standing waves on quantum graphs
• Nonlocal Nonlinear Schrodinger Equation on Metric Graphs
• Dirac Particles in Transparent Quantum Graphs: Tunable transport of relativistic quasiparticles in branched structures
• Exciton dynamics in branched conducting polymers: Quantum graphs based approach
• Reflectionless propagation of Manakov solitons on a line:A model based on the concept of transparent boundary conditions
• Fokker-Planck equation on metric graphs
• Discrete Nonlocal Nonlinear Schroedinger equation on Metric Graphs: Dynamics of PT-Symmetric Solitons in Discrete Networks
• Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks