Asymptotic properties of excited states in the Thomas--Fermi limit (2009)
Excited states are stationary localized solutions of the Gross--Pitaevskii equation with a harmonic potential and a repulsive nonlinear term that have zeros on a real axis. Existence and asymptotic...
On the Thomas-Fermi ground state in a harmonic potential (2009)
Gallo, Clément, Pelinovsky, Dmitry
We study nonlinear ground states of the Gross-Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential. The Thomas-Fermi approximation of ground...
Belmonte-Beitia, Juan, Pelinovsky, Dmitry
We address the Gross--Pitaevskii (GP) equation with a periodic linear potential and a periodic sign-varying nonlinearity coefficient. Contrary to the claims in the previous works of Abdullaev {\em et...
Wave breaking in the short-pulse equation (2009)
Liu, Yue, Pelinovsky, Dmitry, Sakovich, Anton
Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of...
Wave breaking in the Ostrovsky--Hunter equation (2009)
Liu, Yue, Pelinovsky, Dmitry, Sakovich, Anton
The Ostrovsky--Hunter equation governs evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dispersion. Sufficient conditions for the wave breaking in the...
Global well-posedness of the short-pulse and sine-Gordon equations in energy space (2008)
Pelinovsky, Dmitry, Sakovich, Anton
We prove global well-posedness of the short-pulse equation with small initial data in Sobolev space H^s for an integer s>=2. Our analysis relies on local well-posedness results of Schafer and Wayne,...
Eigenvalues of a nonlinear ground state in the Thomas-Fermi approximation (2008)
Gallo, Clément, Pelinovsky, Dmitry
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. Existence of the energy...
MODELING OF WAVE RESONANCES IN LOW-CONTRAST PHOTONIC CRYSTALS ∗ (2008)
Dmitri Agueev, Dmitry Pelinovsky
Abstract. Coupled-mode equations are derived from Maxwell equations for modeling of lowcontrast cubic-lattice photonic crystals in three spatial dimensions. Coupled-mode equations describe resonantly...
Department of Mathematical Sciences, Loughborough University, (2007)
Roger Grimshaw, Dmitry Pelinovsky, E M Pelinovsky, Tatiana Talipova
Wave group dynamics in weakly nonlinear
Pelinovsky, Dmitry, Schneider, Guido
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. Our construction...
Dohnal, Tomas, Pelinovsky, Dmitry, Schneider, Guido
We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in...
Pelinovsky, Dmitry, Schneider, Guido
Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic potential and to approximate localized solutions called gap...
Moving gap solitons in periodic potentials (2007)
Pelinovsky, Dmitry, Schneider, Guido
We address existence of moving gap solitons (traveling localized solutions) in the Gross-Pitaevskii equation with a small periodic potential. Moving gap solitons are approximated by the explicit...
Surface gap solitons at a nonlinearity interface (2007)
Dohnal, Tomas, Pelinovsky, Dmitry
We demonstrate existence of waves localized at the interface of two nonlinear periodic media with different coefficients of the cubic nonlinearity via the one-dimensional Gross--Pitaevsky equation....
Spectrum of a non-self-adjoint operator associated with the periodic heat equation (2007)
Chugunova, Marina, Pelinovsky, Dmitry
We study the spectrum of the linear operator $L = - \partial_{\theta} - \epsilon \partial_{\theta} (\sin \theta \partial_{\theta})$ subject to the periodic boundary conditions on $\theta \in...
Lyapunov--Schmidt reduction algorithm for three-dimensional discrete vortices (2006)
Lukas, Mike, Pelinovsky, Dmitry, Kevrekidis, P. G.
We address persistence and stability of three-dimensional vortex configurations in the discrete nonlinear Schr\"{o}dinger (NLS) equation and develop a symbolic package based on Wolfram's MATHEMATICA...
Comech, Andrew, Cuccagna, Scipio, Pelinovsky, Dmitry
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 instability regions. The...
Chugunova, Marina, Pelinovsky, Dmitry
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 successive iterations...
Translationally invariant nonlinear Schrodinger lattices (2006)
Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation is addressed. The discrete NLS equation with the...
Normal form for travelling kinks in discrete KleinGordon lattices (2006)
Iooss, Gérard, Pelinovsky, Dmitry
We study travelling kinks in the spatial discretizations of the nonlinear KleinGordon equation, which include the discrete 4 lattice and the discrete sine-Gordon lattice. The differential...
Normal form for travelling kinks in discrete Klein-Gordon lattices (2005)
Iooss, Gerard, Pelinovsky, Dmitry
We study travelling kinks in the spatial discretizations of the nonlinear Klein--Gordon equation, which include the discrete $\phi^4$ lattice and the discrete sine--Gordon lattice. The differential...
Instabilities of multi-hump vector solitons in coupled nonlinear Schroedinger equations (2005)
Pelinovsky, Dmitry, Yang, Jianke
Spectral stability of multi-hump vector solitons in the Hamiltonian system of coupled nonlinear Schr\"{o}dinger (NLS) equations is investigated both analytically and numerically. Using the closure...
Spectral stability and time evolution of N-solitons in KdV hierarchy (2005)
Kodama, Yuji, Pelinovsky, Dmitry
This paper concerns spectral stability and time evolution of $N$-solitons in the KdV hierarchy with mixed commuting time flows. Spectral stability problem is analyzed by using a pair of self-adjoint...
Semi-stability of embedded solitons in the general fifth-order KdV equation (2002)
Tan, Yu, Yang, Jianke, Pelinovsky, Dmitry
Evolution of perturbed embedded solitons in the general Hamiltonian fifth-order Korteweg--de Vries (KdV) equation is studied. When an embedded soliton is perturbed, it sheds a one-directional...
Instabilities of dispersion-managed solitons in the normal dispersion regime (2000)
Dispersion-managed solitons are reviewed within a Gaussian variational approximation and an integral evolution model. In the normal regime of the dispersion map (when the averaged path dispersion is...
Wave group dynamics in weakly nonlinear long-wave models (2000)
Grimshaw, Roger H.J., Pelinovsky, Dmitry, Pelinovsky, Efim, Talipova, Tatiana
This is a pre-print. The definitive version: GRIMSHAW, PELINOVSKY, PELINOVSKY AND TALIPOVA, 2001. Wave group dynamics in weakly nonlinear long-wave models. Physica D, 159(1-2), pp.35-57.
Wave group dynamics in weakly nonlinear long-wave models (2000)
Grimshaw, Roger H.J., Pelinovsky, Dmitry, Pelinovsky, Efim, Talipova, Tatiana
This is a pre-print. The definitive version: GRIMSHAW, PELINOVSKY, PELINOVSKY AND TALIPOVA, 2001. Wave group dynamics in weakly nonlinear long-wave models. Physica D, 159(1-2), pp.35-57.