Stationary Nonlinear Schrödinger Equation on Simplest Graphs: Boundary conditions and exact solutions
arXiv:1107.1220 · doi:10.1016/j.physleta.2013.02.011
Abstract
We treat the stationary (cubic) nonlinear Schrödinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs consisting of three bonds. It is shown that the method can be extended for the case of arbitrary number of bonds of star graphs and for other simplest topologies such as tree and loop graphs. The case of repulsive and attractive nonlinearities are treated separately.
References in corpus (20)
- Kirchhoff's Rule for Quantum Wires
- Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
- Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity
- Stationary solutions of the one-dimensional nonlinear Schroedinger equation: II. Case of attractive nonlinearity
- A Waveguide for Bose-Einstein Condensates
- Bose beams: coherent propagation through a guide
- Soliton solutions of nonlinear Schroedinger equation on simple networks
- Fast solitons on star graphs
- On the structure of critical energy levels for the cubic focusing NLS on star graphs
- Stationary scattering from a nonlinear network
- Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides
- Stationary states of the Gross-Pitaevskii equation with linear counterpart
- Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth
- Eigenfunction Statistics on Quantum Graphs
- An analytical study of resonant transport of Bose-Einstein condensates
- Statics and dynamics of BEC's in double square well potentials
- Soliton Propagation in Chains with Simple Nonlocal Defects
- Propagation of Discrete Solitons in Inhomogeneous Networks
- Topological Filters for Solitons in Coupled Waveguides Networks
- Bose-Einstein condensation in random directed networks
Cited by in corpus (15)
- Negative energy ground states for the -critical NLSE on metric graphs
- Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
- Soliton transport in tubular networks: transmission at vertices in the shrinking limit
- Standing waves on quantum graphs
- Dimensional crossover with a continuum of critical exponents for NLS on doubly periodic metric graphs
- Sine-Gordon solitons in networks: Scattering and transmission at vertices
- Dynamics of Dirac solitons in networks
- Transparent nonlinear networks
- Nonlocal Nonlinear Schrodinger Equation on Metric Graphs
- PT-symmetric quantum graphs
- Charged solitons in branched conducting polymers
- Discrete Nonlocal Nonlinear Schroedinger equation on Metric Graphs: Dynamics of PT-Symmetric Solitons in Discrete Networks
- Integrable Defects at Junctions within a Network
- Ground states for the NLS on non-compact graphs with an attractive potential
- Nonlinear standing waves on planar branched systems: Shrinking into metric graph