Discrete travelling solitons in the Salerno model (2008)
Melvin, TRO, Champneys, AR, Pelinovsky, Dmitry E
We investigate travelling solitary waves in the 1D Salerno model, which interpolates between the cubic discrete nonlinear Schrödinger (DNLS) equation and the integrable Ablowitz-Ladik (AL) model. In...
Discrete travelling solitons in the Salerno model (2008)
Melvin, TRO, Champneys, AR, Pelinovsky, Dmitry E
We investigate travelling solitary waves in the 1D Salerno model, which interpolates between the cubic discrete nonlinear Schrödinger (DNLS) equation and the integrable Ablowitz-Ladik (AL) model. In...
One-parameter localized traveling waves in nonlinear Schrodinger lattices (2007)
Pelinovsky, Dmitry E, Melvin, TRO, Champneys, AR
We address traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation. By using the Implicit Function Theorem for solution of the...
One-parameter localized traveling waves in nonlinear Schrodinger lattices (2007)
Pelinovsky, Dmitry E, Melvin, TRO, Champneys, AR
We address traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation. By using the Implicit Function Theorem for solution of the...
One-parameter localized traveling waves in nonlinear Schrodinger lattices (2007)
Pelinovsky, Dmitry E, Melvin, TRO, Champneys, AR
We address traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation. By using the Implicit Function Theorem for solution of the...
Dark solitons in external potentials (2006)
Pelinovsky, Dmitry E., Kevrekidis, Panayotis G.
We consider the persistence and stability of dark solitons in the Gross-Pitaevskii (GP) equation with a small decaying potential. We show that families of black solitons with zero speed originate...
Feshbach resonance management of Bose-Einstein condensates in optical lattices (2006)
Porter, Mason A., Chugunova, Marina, Pelinovsky, Dmitry E.
We analyze gap solitons in trapped Bose-Einstein condensates (BECs) in optical lattice potentials under Feshbach resonance management. Starting with an averaged Gross-Pitaevsky equation with a...
Incompressible viscous fluid flows in a thin spherical shell (2006)
Ibragimov, Ranis N., Pelinovsky, Dmitry E.
Linearized stability of incompressible viscous fluid flows in a thin spherical shell is studied by using the two-dimensional Navier--Stokes equations on a sphere. The stationary flow on the sphere...
Feshbach Resonance Management of Bose-Einstein Condensates in Optical Lattices (2005)
Porter, Mason A., Chugunova, Marina, Pelinovsky, Dmitry E.
We analyze gap solitons in trapped Bose-Einstein condensates (BECs) in optical lattice potentials under Feshbach resonance management. Starting with an averaged Gross-Pitaevsky (GP) equation with a...
Translationally invariant discrete kinks from one-dimensional maps (2005)
Barashenkov, I. V., Oxtoby, O. F., Pelinovsky, Dmitry E.
For most discretisations of the $\phi^4$ theory, the stationary kink can only be centered either on a lattice site or midway between two adjacent sites. We search for exceptional discretisations...
Oscillations of dark solitons in trapped Bose-Einstein condensates (2005)
Pelinovsky, Dmitry E., Frantzeskakis, D. J., Kevrekidis, P. G.
We consider a one-dimensional defocusing Gross--Pitaevskii equation with a parabolic potential. Dark solitons oscillate near the center of the potential trap and their amplitude decays due to...
Spatial vector solitons in nonlinear photonic crystal fibers (2005)
Salgueiro, Jose R., Kivshar, Yuri S., Pelinovsky, Dmitry E., Simon, Veronica, Michinel, Humberto
We study spatial vector solitons in a photonic crystal fiber (PCF) made of a material with the focusing Kerr nonlinearity. We show that such two-component localized nonlinear waves consist of two...
Bifurcations and stability of gap solitons in periodic potentials (2004)
Pelinovsky, Dmitry E., Sukhorukov, Andrey A., Kivshar, Yuri S.
We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrodinger equation with a sinusoidal potential, such as photonic...
Stable vortex and dipole vector solitons in a saturable nonlinear medium (2002)
Yang, Jianke, Pelinovsky, Dmitry E.
We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation...
Stability criterion for multi-component solitary waves (2000)
Pelinovsky, Dmitry E., Kivshar, Yuri S.
We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of $N$ incoherently coupled nonlinear Schrodinger equations. Soliton...
Internal Oscillations and Radiation Damping of Vector Solitons (1999)
Internal modes of vector solitons and their radiation-induced damping are studied analytically and numerically in the framework of coupled nonlinear Schrodinger equations. Bifurcations of internal...
Spectral decomposition for the Dirac system associated to the DSII equation (1999)
Pelinovsky, Dmitry E., Sulem, Catherine
A new (scalar) spectral decomposition is found for the Dirac system in two dimensions associated to the focusing Davey--Stewartson II (DSII) equation. Discrete spectrum in the spectral problem...