2022/06/19 by Bal, Guillaume
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2206.09439
We analyze the propagation of two-dimensional dispersive and relativistic wavepackets localized in the vicinity of the zero level set Γ of a domain wall. The main applications we consider are a topologically non-trivial Dirac model and a similar but topologically trivial Klein-Gordon equation. The static domain wall models an interface separating two insulating media in possibly different topological phases. We propose a semiclassical oscillatory representation of the wavepackets and provide an estimate of their accuracy in appropriate energy norms. We describe the propagation of relativistic modes along Γ and analyze dispersive modes by a stationary phase method. In the absence of turning points, we show that arbitrary localized and smooth initial conditions may be represented as a superposition of such wavepackets. In the presence of turning points, the results apply only for sufficiently high-frequency wavepackets.