The Eigenvalue Problem of Nonlinear Schrödinger Equation at Dirac Points of Honeycomb Lattice

2022/02/12 by Chen, Yejia, Peng, Ruihan, Fu, Qidong +2
#35P30 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph) #Optics (physics.optics) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2202.06099

Abstract

We give a rigorous deduction of the eigenvalue problem of the nonlinear Schrödinger 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 Schrödinger equation. We give the existence, the way of construction, uniqueness in H² space and the C^∞ continuity of these eigenfunctions.

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