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 (5)
- Fast solitons on star graphs
- On the structure of critical energy levels for the cubic focusing NLS on star graphs
- Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides
- An analytical study of resonant transport of Bose-Einstein condensates
- Soliton Propagation in Chains with Simple Nonlocal Defects
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