Stationary real solutions of the nonlinear Schr ̈odinger equation on a ring with a defect
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概要
Stationary real solutions of the nonlinear Schr ̈odinger equation on a ring with a defect
by Axel Perez-Obiol and Taksu Cheon
Abstract:
We analyze the 1D cubic nonlinear stationary Schro ̈dinger equation on a ring with a defect for both focusing and defocusing nonlinearity. All possible δ and δ′ boundary conditions are considered at the defect, computing for each of them the real eigenfunctions, written as Jacobi elliptic functions, and eigenvalues for the ground state and first few excited energy levels. All six independent Jacobi elliptic functions are found to be solutions of some boundary condition. We also provide a way to map all eigenfunctions satisfying δ/δ′ conditions to any other general boundary condition or point-like potential.
[Last update Aug. 3, 2018 arXiv submission version]
Dynamical Galam model
by Taksu Cheon and Serge Galam
Abstract:
We introduce a model of temporal evolution of political opinions which amounts to a dynamical extension of Galam model in which the number of inflexibles are treated as dynamical variables. We find that the critical value of inflexibles in the original Galam model now turns into a fixed point of the system whose stability controls the phase trajectory of the political opinions. The appearance of two phases is found, in which majority-preserving and regime-changing limit cycles are respectively dominant, and the phase transition between them is observed.
Post arXiv version: referees' comments incorporated
[last update : Apr 20, 2018, 12:00, v5.0C, with critical typo corrections on eqs(4)-(6) over published version & arXiv version]
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