195 citations · 1.2k across the 66 of their papers we have counts for
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Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones
Denis Borisov, Konstantin Pankrashkin
We consider small perturbations of the Laplace operator in a multi-dimensional cylindrical domain by second order differential operators with periodic coefficients. We show that un…
Formally self-adjoint quasi-differential operators and boundary value problems
Andrii Goriunov, Vladimir Mikhailets, Konstantin Pankrashkin
We develop the machinery of boundary triplets for one-dimensional operators generated by formally self-adjoint quasi-differential expression of arbitrary order on a finite interval…
Gap opening and split band edges in waveguides coupled by a periodic system of small windows
D. Borisov, K. Pankrashkin
At the example of two coupled waveguides we construct a periodic second order differential operator acting in a Euclidean domain and having spectral gaps whose edges are attained s…