A perturbative extension of the J-matrix method yields scattering matrices for the 2D nonlinear Schrödinger equation with ψ³ and ψ⁵ nonlinearities, exhibiting bifurcations at specific energies.
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Two-parameter families of exactly solvable quantum systems are constructed via tridiagonal representations, producing energy-dependent orthogonal polynomials and potentials that can induce bound states from continuous spectra when parameters exceed critical values.
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Perturbative nonlinear J-matrix method of scattering in two dimensions
A perturbative extension of the J-matrix method yields scattering matrices for the 2D nonlinear Schrödinger equation with ψ³ and ψ⁵ nonlinearities, exhibiting bifurcations at specific energies.
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Two-parameter classes of exactly solvable quantum systems
Two-parameter families of exactly solvable quantum systems are constructed via tridiagonal representations, producing energy-dependent orthogonal polynomials and potentials that can induce bound states from continuous spectra when parameters exceed critical values.