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nlin.PS2008
Asymptotic stability of small solitons in the discrete nonlinear Schrodinger equation in one dimension
P. G. Kevrekidis, D. E. Pelinovsky, A. Stefanov
Asymptotic stability of small solitons in one dimension is proved in the framework of a discrete nonlinear Schrodinger equation with septic and higher power-law nonlinearities and…
math-ph2008
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…
math-ph2008★ 50 cited
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_{…