Name
Title | ||
|---|---|---|
Wave Packets In The Fractional Nonlinear Schrodinger Equation With A Honeycomb Potential |
Abstract | ||
|---|---|---|
In this article, we study wave dynamics in the fractional nonlinear Schrodinger equation with a modulated honeycomb potential. This problem arises from recent research interests in the interplay between topological materials and nonlocal governing equations. We first develop the Floquet-Bloch spectral theory of the linear fractional Schrodinger operator with a honeycomb potential. Especially, we prove the existence of conically degenerate points, i.e., Dirac points, at which two dispersion band functions intersect. We then investigate the dynamics of wave packets spectrally localized at a Dirac point and derive the leading effective envelope equation. It turns out the envelope can be described by a nonlinear Dirac equation with a varying mass. With rigorous error estimates, we demonstrate that the asymptotic solution based on the effective envelope equation approximates the true solution well in the weighted-H-8 space. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1137/20M1340757 | MULTISCALE MODELING & SIMULATION |
Keywords | DocType | Volume |
fractional Schrodinger equation, honeycomb structure, effective dynamics | Journal | 19 |
Issue | ISSN | Citations |
2 | 1540-3459 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |