170 citations · 421 across the 26 of their papers we have counts for
4 papers · 1 filter
Survey on global existence in the nonlinear Dirac equations in one dimension
Dmitry Pelinovsky
We consider the nonlinear Dirac equations in one dimension and review various results on global existence of solutions in H1. Depending on the character of the nonlinear terms, exi…
Eigenvalues of a nonlinear ground state in the Thomas-Fermi approximation
Clément Gallo, Dmitry Pelinovsky
We study a nonlinear ground state of the Gross-Pitaevskii equation with a parabolic potential in the hydrodynamics limit often referred to as the Thomas--Fermi approximation. Exist…
On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension
D. E. Pelinovsky, A. Stefanov
Based on the recent work \cite{KKK} for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator $$ H ϕ= (-\De + V)ϕ=-(ϕ_{n+1} + ϕ_{…
Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential
Dmitry Pelinovsky, Guido Schneider
We justify the validity of the discrete nonlinear Schrodinger equation for the tight-binding approximation in the context of the Gross-Pitaevskii equation with a periodic potential…