10 citations · 27 across the 12 of their papers we have counts for
13 papers
Resonant Solutions of the Non-linear Schroedinger Equation with Periodic Potential
A. Duaibes, Yu. Karpeshina
The goal is a construction of stationary solutions close to a non-trivial combination of two plane waves at high energies for a periodic non-linear Schroedinger equation in dimensi…
Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Three
Yulia Karpeshina, Seonguk Kim, Roman Shterenberg
Quasi-periodic solutions of the Gross-Pitaevskii equation with a periodic potential in dimension three are studied. It is proven that there is an extensive "non-resonant" set ${\ma…
Ballistic Transport for Schrödinger Operators with Quasi-periodic Potentials
Yulia Karpeshina, Leonid Parnovski, Roman Shterenberg
We prove the existence of ballistic transport for a Schrödinger operator with a generic quasi-periodic potential in any dimension .
Bethe-Sommerfeld Conjecture and Absolutely Continuous Spectrum of Multi-Dimensional Quasi-Periodic Schrödinger Operators
Yulia Karpeshina, Leonid Parnovski, Roman Shterenberg
We consider Schrödinger operators in , , with quasi-periodic potentials . We prove that the absolutely continuous spect…
Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Two
Yulia Karpeshina, Seonguk Kim, Roman Shterenberg
Quasi-periodic solutions of a nonlinear polyharmonic equation for the case in , , are studied. This includes Gross-Pitaevskii equation in dimension two ($l=1,n=…
Solutions of Nonlinear Polyharmonic Equation with Periodic Potential
Yulia Karpeshina, Seonguk Kim
Quasi-periodic solutions of a nonlinear periodic polyharmonic equation in , , are studied. It is proven that there is an extensive "non-resonant" set ${\mathcal G}\subse…