Perturbative nonlinear J-matrix method of scattering in two dimensions

• URL: http://arxiv.org/abs/2511.14519v1
• Date: Tue, 18 Nov 2025 14:15:26 GMT
• Title: Perturbative nonlinear J-matrix method of scattering in two dimensions
• Authors: T. J. Taiwo, A. D. Alhaidari, U. Al Khawaja,
• Abstract summary: We obtain the scattering matrix for the time-independent nonlinear Schrdinger equation in two dimensions with circular symmetry.<n>We present the theory for a general 2n 1 nonlinearity, where n is a natural number.<n>At certain value(s) of the energy, we observe the occurrence of bifurcation with two stable solutions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a perturbative formulation for a nonlinear extension of the J-matrix method of scattering in two dimensions. That is, we obtain the scattering matrix for the time-independent nonlinear Schrödinger equation in two dimensions with circular symmetry. The formulation relies on the linearization of products of orthogonal polynomials and on the utilization of the tools of the J-matrix method. Gauss quadrature integral approximation is instrumental in the numerical implementation of the approach. We present the theory for a general ψ^{2n + 1} nonlinearity, where n is a natural number, and obtain results for the cubic and quintic nonlinearities, ψ^3 and ψ^5. At certain value(s) of the energy, we observe the occurrence of bifurcation with two stable solutions. This curious and interesting phenomenon is a clear signature and manifestation of the underlying nonlinearity.

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