论文标题
蜂窝晶格的狄拉克点的非线性schrödinger方程的特征值问题
The Eigenvalue Problem of Nonlinear Schrödinger Equation at Dirac Points of Honeycomb Lattice
论文作者
论文摘要
我们严格扣除了迪拉克点的非线性schrödinger方程（NLS）的特征值问题，以实现蜂窝状晶格对称性的潜力。基于引导法方法，我们将本征函数分叉分为八个不同的模式，从回归线性schrödinger方程的二维退化特征空间。我们给出了这些特征函数的$ h^2 $空间的存在，构建方式，唯一性和$ c^\ infty $连续性。
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 $H^2$ space and the $C^\infty$ continuity of these eigenfunctions.
