170 citations · 400 across the 22 of their papers we have counts for
6 papers · 1 filter
Dark solitons in external potentials
Dmitry E. Pelinovsky, Panayotis G. Kevrekidis
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…
Lyapunov--Schmidt reduction algorithm for three-dimensional discrete vortices
Mike Lukas, Dmitry Pelinovsky, P. G. Kevrekidis
We address persistence and stability of three-dimensional vortex configurations in the discrete nonlinear Schrödinger (NLS) equation and develop a symbolic package based on Wolfram…
Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation
Andrew Comech, Scipio Cuccagna, Dmitry Pelinovsky
We prove the instability of a ``critical'' solitary wave of the generalized Korteweg -- de Vries equation, the one with the speed at the border between the stability and instabilit…
Incompressible viscous fluid flows in a thin spherical shell
Ranis N. Ibragimov, Dmitry E. Pelinovsky
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 fl…
Two-pulse solutions in the fifth-order KdV equation : rigorous theory and numerical approximations
Marina Chugunova, Dmitry Pelinovsky
We revisit existence and stability of two-pulse solutions in the fifth-order Korteweg--de Vries (KdV) equation with two new results. First, we modify the Petviashvili method of suc…
Translationally invariant nonlinear Schrodinger lattices
Dmitry Pelinovsky
Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation is addressed. The discrete NLS…