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We consider localized modes (discrete breathers) of the discrete nonlinear SchrÃ¶dinger equation in dt = Ïˆn+1 + Ïˆnâˆ’1 âˆ’ 2Ïˆn + Ïƒ|Ïˆn|Ïˆn, Ïƒ = Â±1, n âˆˆ Z. We study the diversity of the steady-stateâ€¦ (More)

- Georgy L Alfimov, Panayotis G. Kevrekidis, Vladimir V. Konotop, Mario Salerno
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2002

In the present paper we use the Wannier function basis to construct lattice approximations of the nonlinear SchrÃ¶dinger equation with a periodic potential. We show that the nonlinear SchrÃ¶dingerâ€¦ (More)

Received (received date) Revised (revised date) We consider several effects of the matter wave dynamics which can be observed in Bose-Einstein condensates embedded into optical lattices. Forâ€¦ (More)

- Dmitry A. Zezyulin, Vladimir V. Konotop
- Physical review letters
- 2012

By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to suchâ€¦ (More)

- G. Perla Menzala, Vladimir V. Konotop, Av. Getulio Vargas
- 2008

We prove global existence and uniqueness of solutions of some important nonlinear lattices which include the Fermi-Pasta-Ulam (FPU) lattice. Our result shows (on a particular example) that the FPUâ€¦ (More)

We show that the phenomenon of modulational instability in arrays of Bose-Einstein condensates confined to optical lattices gives rise to coherent spatial structures of localized excitations. Theseâ€¦ (More)

- Panayotis G. Kevrekidis, Vladimir V. Konotop
- Mathematics and Computers in Simulation
- 2003

In this short communication we study compactons in the setting of discrete nonlinear Kleinâ€“Gordon (DNKG) chains. The temporal and spatial dependences of the solutions are separated resulting in anâ€¦ (More)

- Fatkhulla Kh Abdullaev, Yu V. Bludov, S. V. Dmitriev, Panayotis G. Kevrekidis, Vladimir V. Konotop
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2008

It is shown that the tight-binding approximation of the nonlinear SchrÃ¶dinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number ofâ€¦ (More)

- A. V. Yulin, Vladimir V. Konotop
- Optics letters
- 2013

Stable discrete compactons in interconnected three-line waveguide arrays are found in linear and nonlinear limits in conservative and in parity-time (PT)-symmetric models. The compactons result fromâ€¦ (More)

- Dmitry A. Zezyulin, Vladimir V. Konotop, Fatkhulla Kh Abdullaev
- Optics letters
- 2012

We report on existence and properties of discrete solitons in arrays of alternating waveguides with positive and negative refractive indices. When the nonlinearities of all waveguides are focusing,â€¦ (More)