Mixed Fourier-Legendre Spectral Methods for the Multiple Solutions of the Schrodinger Equation on the Unit Disk
Abstract
In this paper, we first compute the multiple non-trivial solutions of the Schrodinger 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 extended systems, which can detect the symmetry-breaking bifurcation points on the branch of the O(2) symmetric positive solutions. We also compute the multiple positive solutions with various symmetries of the Schrodinger equation by the branch switching method based on the Liapunov-Schmidt reduction. Finally, the bifurcation diagrams are constructed, showing the symmetry/peak breaking phenomena of the Schr¨odinger equation. Numerical results demonstrate the effectiveness of these approaches.
Keywords:
approximation algorithm, bifurcation diagrams, multiple solutions, computational experiment, positive solutionHow to Cite
Share
License
Copyright (c) 2017 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
View article in other formats
Published
Issue
Section
Copyright
Copyright (c) 2017 The Author(s). Published by Vilnius Gediminas Technical University.
License
This work is licensed under a Creative Commons Attribution 4.0 International License.