The Eigenvalue Problem of Nonlinear Schr\'odinger Equation at Dirac Points of Honeycomb Lattice

Autor:	Chen, Yejia, Peng, Ruihan, Fu, Qidong, Ye, Fangwei, Luo, Weidong
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs Condensed Matter - Materials Science Mathematical Physics Physics - Optics Quantum Physics 35P30 35Q55
Druh dokumentu:	Working Paper
Popis:	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 $H^2$ space and the $C^\infty$ continuity of these eigenfunctions. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.06099 Zobrazit plný text záznamu View this record from Arxiv