Mixed Fourier-Legendre Spectral Methods for the Multiple Solutions of the Schrödinger Equation on the Unit Disk

• Published in: Mathematical modelling and analysis Vol. 22; no. 2; pp. 167 - 185
• Main Authors: Li, Zhao-Xiang, Laob, Ji, Wang, Zhong-Qing
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 04.03.2017; Vilnius Gediminas Technical University
• Subjects: approximation algorithm; bifurcation diagrams; Bifurcation theory; Bifurcations; computational experiment; Disks; Mathematical models; Mathematical research; multiple solutions; positive solution; Reduction; Schroedinger equation; Schrödinger equation; Spectra; Spectral decomposition (Mathematics); Spectral methods; Symmetry; approximation algorithm; positive solution; multiple solutions; computational experiment; bifurcation diagrams

In this paper, we first compute the multiple non-trivial solutions of the Schrödinger equation on a unit disk, by using the Liapunov-Schmidt reduction and symmetry-breaking bifurcation theory, combined with the mixed Fourier-Legendre spectral and pseudospectral methods. After that, we propose the ex...