Green's Function Formulation of Multiple Nonlinear Dirac $\delta$-Function Potential in One Dimension

Abstract

In this work, we study the scattering problem of the general nonlinear finitely many Dirac delta potentials with complex coupling constants (or opacities in the context of optics) using the Green's function method and then find the bound state energies and the wave functions for the particular form of the nonlinearity in the case of positive real coupling constants.

13 pages, published version

References in corpus (6)

• Sinc approximation of algebraically decaying functions
• Spontaneous symmetry breaking in a nonlinear double-well structure
• Matter-wave soliton interferometer based on a nonlinear splitter
• The attractive nonlinear delta-function potential
• Nonlinear Scattering and Its Transfer Matrix Formulation in One Dimension
• Point interactions with bias potentials

Cited by in corpus (2)

• Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian
• The Harmonic Oscillator Potential Perturbed by a Combination of Linear and Non-linear Dirac Delta Interactions with Application to Bose-Einstein Condensation