The Eigenvalue Problem of Nonlinear Schr\"odinger Equation at Dirac Points of Honeycomb Lattice
Analysis of PDEs
2022-02-15 v1 Materials Science
Mathematical Physics
math.MP
Optics
Quantum Physics
Abstract
We give a rigorous deduction of the eigenvalue problem of the nonlinear Schr\"odinger equation (NLS) at Dirac Points for potential of honeycomb lattice symmetry. Based on a bootstrap method, we observe the bifurcation of the eigenfunctions into eight distinct modes from the two-dimensional degenerated eigenspace of the regressive linear Schr\"odinger equation. We give the existence, the way of construction, uniqueness in space and the continuity of these eigenfunctions.
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Cite
@article{arxiv.2202.06099,
title = {The Eigenvalue Problem of Nonlinear Schr\"odinger Equation at Dirac Points of Honeycomb Lattice},
author = {Yejia Chen and Ruihan Peng and Qidong Fu and Fangwei Ye and Weidong Luo},
journal= {arXiv preprint arXiv:2202.06099},
year = {2022}
}
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28 pages