Related papers: The Eigenvalue Problem of Nonlinear Schr\"odinger Equation at Dirac Points of Honeycomb Lattice

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

URL: http://arxiv.org/abs/2202.06099v1
Date: Sat, 12 Feb 2022 16:46:52 GMT
Title: The Eigenvalue Problem of Nonlinear Schr\"odinger Equation at Dirac Points of Honeycomb Lattice
Authors: Yejia Chen, Ruihan Peng, Qidong Fu, Fangwei Ye and Weidong Luo
Abstract summary: 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. We observe the bifurcation of the eigenfunctions into eight distinct modes from the two-dimensional degenerated eigenspace of the regressive linear Schr"odinger equation.
Score: 4.549831511476248
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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 $H^2$ space and the $C^\infty$ continuity of these eigenfunctions.

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