Dr Dmitry Pelinovsky
McMaster University
Professor, Mathematics
Canada
My co-authors include
Professor Roger H J Grimshaw
Dr Oleg N Kirillov
My Publications
Normal form for transverse instability of the line soliton with a nearly critical speed...
Mathematical Modelling of Natural Phenomena
January 2018
Orbital stability in the cubic defocusing NLS equation: II. The black soliton
Journal of Differential Equations
May 2015
Orbital stability in the cubic defocusing NLS equation: I. Cnoidal periodic waves
Journal of Differential Equations
May 2015
Persistence of the Thomas–Fermi approximation for ground states of the Gross–Pitaevskii...
Applied Mathematics Letters
February 2015
On numerical modelling and the blow-up behavior of contact lines with a $$\mathbf{180}^...
Journal of Engineering Mathematics
January 2015
On the orbital stability of Gaussian solitary waves in the log-KdV equation
Nonlinearity
November 2014
On the Thomas-Fermi Approximation of the Ground State in a PT-Symmetric Confining Poten...
Studies in Applied Mathematics
September 2014
Domain Walls in the Coupled Gross–Pitaevskii Equations
Archive for Rational Mechanics and Analysis
September 2014
Stability of multi-solitons in the cubic NLS equation
Journal of Hyperbolic Differential Equations
June 2014
Short-wave transverse instabilities of line solitons of the two-dimensional hyperbolic ...
Theoretical and Mathematical Physics
April 2014
Validity of the Weakly Nonlinear Solution of the Cauchy Problem for the Boussinesq-Type...
Studies in Applied Mathematics
March 2014
Nonlinear modes in a generalized $\mathcal{PT}$-symmetric discrete nonlinear Schrödinge...
Journal of Physics A Mathematical and Theoretical
February 2014
Spectral Stability of Nonlinear Waves in KdV-Type Evolution Equations
February 2014
Wave Systems with an Infinite Number of Localized Traveling Waves
Physical Review Letters
February 2014
Justification of the log--KdV Equation in Granular Chains: The Case of Precompression
SIAM Journal on Mathematical Analysis
January 2014
The asymptotic stability of solitons in the cubic NLS equation on the line
Applicable Analysis
December 2013
Nonlinear Physical Systems
November 2013
Stability of Discrete Breathers in Magnetic Metamaterials
October 2013
Universal power law for the energy spectrum of breaking Riemann waves
JETP Letters
October 2013
Orbital Stability of Dirac Solitons
Letters in Mathematical Physics
August 2013
Nonlinear dynamics in PT-symmetric lattices
Journal of Physics A Mathematical and Theoretical
August 2013
Global existence of small-norm solutions in the reduced Ostrovsky equation
Discrete and Continuous Dynamical Systems
August 2013
Nonlinear Stationary States in PT-Symmetric Lattices
SIAM Journal on Applied Dynamical Systems
July 2013
On transverse stability of discrete line solitons
Physica D Nonlinear Phenomena
July 2013
Matter-Wave Bright Solitons in Spin-Orbit Coupled Bose-Einstein Condensates
Physical Review Letters
June 2013
Justification of a nonlinear Schrödinger model for laser beams in photopolymers
Zeitschrift für angewandte Mathematik und Physik
May 2013
Periodic Traveling Waves in Diatomic Granular Chains
Journal of Nonlinear Science
February 2013
Lattice Differential Equations
Oberwolfach Reports
January 2013
\chem{\mathcal {P}\mathcal {T}} -symmetric lattices with spatially extended gain/loss a...
EPL (Europhysics Letters)
January 2013
Multilevel computations of dispersed drug release
Numerical Methods for Partial Differential Equations
December 2012
Discrete solitons in \chem {\cal PT} -symmetric lattices
EPL (Europhysics Letters)
December 2012
Rigorous justification of the short-pulse equation
Nonlinear Differential Equations and Applications NoDEA
November 2012
Multi-site breathers in Klein–Gordon lattices: stability, resonances and bifurcations
Nonlinearity
November 2012
Normal form for the symmetry-breaking bifurcation in the nonlinear Schrödinger equation
Journal of Differential Equations
November 2012
Bifurcations of Asymmetric Vortices in Symmetric Harmonic Traps
Applied Mathematics Research eXpress
October 2012
Sharp bounds on enstrophy growth in the viscous Burgers equation
Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences
July 2012
Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimens...
Physical Review E
February 2012
Asymptotic stability of small gap solitons in nonlinear Dirac equations
Journal of Mathematical Physics
January 2012
Preface
Discrete and Continuous Dynamical Systems - Series S
January 2012
Enstrophy growth in the viscous Burgers equation
Dynamics of Partial Differential Equations
January 2012
Breather continuation from infinity in nonlinear oscillator chains
Discrete and Continuous Dynamical Systems
January 2012
On the validity of the variational approximation in discrete nonlinear Schrödinger equa...
Physica D Nonlinear Phenomena
January 2012
On the asymptotic stability of localized modes in the discrete nonlinear Schrödinger eq...
Discrete and Continuous Dynamical Systems - Series S
January 2012
Polychromatic Solitary Waves in a Periodic and Nonlinear Maxwell System
SIAM Journal on Applied Dynamical Systems
January 2012
Paradoxical transitions to instabilities in hydromagnetic Couette-Taylor flows
Physical Review E
December 2011
Symmetry-Breaking Bifurcation in the Nonlinear Schrödinger Equation with Symmetric Pote...
Communications in Mathematical Physics
October 2011
Loops of Energy Bands for Bloch Waves in Optical Lattices
Studies in Applied Mathematics
October 2011
Propagation failure in the discrete Nagumo equation
Proceedings of the American Mathematical Society
October 2011
Backlund Transformation and L2-stability of NLS Solitons
International Mathematics Research Notices
June 2011
Convergence of the Adomian decomposition method for initial-value problems
Numerical Methods for Partial Differential Equations
April 2011
Variational approximations of trapped vortices in the large-density limit
Nonlinearity
March 2011
Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation
Physica D Nonlinear Phenomena
February 2011
Regularized shock solutions in coating flows with small surface tension
Physics of Fluids
January 2011
Traveling Monotonic Fronts in the Discrete Nagumo Equation
Journal of Dynamics and Differential Equations
December 2010
Homogenization of the variable-speed wave equation
Wave Motion
December 2010
Variational approximations of bifurcations of asymmetric solitons in cubic-quintic nonl...
Discrete and Continuous Dynamical Systems - Series S
December 2010
Asymptotic properties of excited states in the Thomas–Fermi limit
Nonlinear Analysis
October 2010
Bifurcation of gap solitons in periodic potentials with a periodic sign-varying nonline...
Applicable Analysis
September 2010
Excited states in the large density limit: a variational approach
Nonlinearity
June 2010
Global Well-Posedness of the Short-Pulse and Sine–Gordon Equations in Energy Space
Communications in Partial Differential Equations
March 2010
Distribution of eigenfrequencies for oscillations of the ground state in the Thomas-Fer...
Physical Review A
February 2010
Bounds on the tight-binding approximation for the Gross–Pitaevskii equation with a peri...
Journal of Differential Equations
February 2010
Effects of rotation on stability of viscous stationary flows on a spherical surface
Physics of Fluids
January 2010
Count of eigenvalues in the generalized eigenvalue problem
Journal of Mathematical Physics
January 2010
Wave Breaking in the Ostrovsky–Hunter Equation
SIAM Journal on Mathematical Analysis
January 2010
On the uniform convergence of the Chebyshev interpolants for solitons
Mathematics and Computers in Simulation
December 2009
On quadratic eigenvalue problems arising in stability of discrete vortices
Linear Algebra and its Applications
August 2009
Eigenvalues of a nonlinear ground state in the Thomas–Fermi approximation
Journal of Mathematical Analysis and Applications
July 2009
Localization in Periodic Potentials
January 2009
Wave breaking in the short-pulse equation
Dynamics of Partial Differential Equations
January 2009
Discrete Traveling Solitons in the Salerno Model
SIAM Journal on Applied Dynamical Systems
January 2009
Asymptotic Stability of Small Bound States in the Discrete Nonlinear Schrödinger Equation
SIAM Journal on Mathematical Analysis
January 2009
Three-dimensional gravity waves in a channel of variable depth
Communications in Nonlinear Science and Numerical Simulation
December 2008
Justification of the Lattice Equation for a Nonlinear Elliptic Problem with a Periodic ...
Communications in Mathematical Physics
October 2008
Moving gap solitons in periodic potentials
Mathematical Methods in the Applied Sciences
September 2008
Slow-light dispersion in coupled periodic waveguides
Journal of the Optical Society of America B
September 2008
Coupled-Mode Equations and Gap Solitons in a Two-Dimensional Nonlinear Elliptic Problem...
Journal of Nonlinear Science
September 2008
Spectrum of a non-self-adjoint operator associated with the periodic heat equation
Journal of Mathematical Analysis and Applications
June 2008
Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations
Journal of Mathematical Sciences
June 2008
Periodic oscillations of discrete NLS solitons in the presence of diffraction management
Nonlinearity
May 2008
Stability of discrete dark solitons in nonlinear Schrödinger lattices
Journal of Physics A Mathematical and Theoretical
April 2008
Lyapunov–Schmidt reduction algorithm for three-dimensional discrete vortices
Physica D Nonlinear Phenomena
March 2008
Kadomtsev-Petviashvili equation
Scholarpedia
January 2008
Periodic oscillations of dark solitons in parabolic potentials
January 2008
Surface Gap Solitons at a Nonlinearity Interface
SIAM Journal on Applied Dynamical Systems
January 2008
On the spectral theory and dispersive estimates for a discrete Schrödinger equation in...
Journal of Mathematical Physics
January 2008
One-parameter localized traveling waves in nonlinear Schrödinger lattices
Physica D Nonlinear Phenomena
December 2007
Justification of the coupled-mode approximation for a nonlinear elliptic problem with a...
Applicable Analysis
August 2007
Two-pulse solutions in the fifth-order KdV equation: Rigorous theory and numerical appr...
Discrete and Continuous Dynamical Systems - Series B
August 2007
Incompressible Viscous Fluid Flows in a Thin Spherical Shell
Journal of Mathematical Fluid Mechanics
July 2007
Dark solitons in external potentials
Zeitschrift für angewandte Mathematik und Physik
June 2007
Nonlinear Instability of a Critical Traveling Wave in the Generalized Korteweg–de Vries...
SIAM Journal on Mathematical Analysis
January 2007
Translationally invariant nonlinear Schrödinger lattices
Nonlinearity
October 2006
Feshbach resonance management of Bose-Einstein condensates in optical lattices
Physical Review E
September 2006
Exact conditions for existence of homoclinic orbits in the fifth-order KdV model
Nonlinearity
August 2006
Discrete vector on-site vortices
Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences
April 2006
Normal form for travelling kinks in discrete Klein–Gordon lattices
Physica D Nonlinear Phenomena
April 2006
Transverse instabilities of deep-water solitary waves
Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences
February 2006
Block-Diagonalization of the Symmetric First-Order Coupled-Mode System
SIAM Journal on Applied Dynamical Systems
January 2006
Eigenvalues of zero energy in the linearized NLS problem
Journal of Mathematical Physics
January 2006
Parametric resonance of ground states in the nonlinear Schrödinger equation
Journal of Differential Equations
January 2006
Nonlinearity management in higher dimensions
Journal of Physics A Mathematical and General
December 2005
Stability of discrete solitons in nonlinear Schrödinger lattices
Physica D Nonlinear Phenomena
December 2005
Persistence and stability of discrete vortices in nonlinear Schrödinger lattices
Physica D Nonlinear Phenomena
December 2005
Travelling kinks in discrete phi 4 models
Nonlinearity
November 2005
Evans Function for Lax Operators with Algebraically Decaying Potentials
Journal of Nonlinear Science
October 2005
Translationally invariant discrete kinks from one-dimensional maps
Physical Review E
September 2005
Spatial Vector Solitons in Nonlinear Photonic Crystal Fibers
Studies in Applied Mathematics
August 2005
Oscillations of dark solitons in trapped Bose-Einstein condensates
Physical Review E
July 2005
Instabilities of Multihump Vector Solitons in Coupled Nonlinear Schrödinger Equations
Studies in Applied Mathematics
July 2005
Spectral stability and time evolution of N -solitons in the KdV hierarchy
Journal of Physics A Mathematical and General
June 2005
Bifurcations of travelling wave solutions in the discrete NLS equations
Physica D Nonlinear Phenomena
March 2005
Solitons in nonintegrable systems
Chaos An Interdisciplinary Journal of Nonlinear Science
January 2005
Averaging of nonlinearity-managed pulses
Chaos An Interdisciplinary Journal of Nonlinear Science
January 2005
Stability analysis of embedded solitons in the generalized third-order nonlinear Schrö...
Chaos An Interdisciplinary Journal of Nonlinear Science
January 2005
Modeling of Wave Resonances in Low-Contrast Photonic Crystals
SIAM Journal on Applied Mathematics
January 2005
Bifurcations from the endpoints of the essential spectrum in the linearized nonlinear S...
Journal of Mathematical Physics
January 2005
Hamiltonian averaging for solitons with nonlinearity management
Physical Review E
October 2004
Bifurcations and stability of gap solitons in periodic potentials
Physical Review E
September 2004
Parametric Resonance and Radiative Decay of Dispersion-Managed Solitons
SIAM Journal on Applied Mathematics
January 2004
Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationar...
SIAM Journal on Numerical Analysis
January 2004
Spectra of positive and negative energies in the linearized NLS problem
Communications on Pure and Applied Mathematics
January 2004
Averaging for Solitons with Nonlinearity Management
Physical Review Letters
December 2003
Purely nonlinear instability of standing waves with minimal energy
Communications on Pure and Applied Mathematics
September 2003
Stability Analysis of Stationary Light Transmission in Nonlinear Photonic Structures
Journal of Nonlinear Science
August 2003
On the exchange of energy in coupled Klein–Gordon equations
Wave Motion
June 2003
Gauge transformation and spectral decomposition for the Ishimori-II equations
Journal of Physics A Mathematical and General
May 2003
Stable all-optical limiting in nonlinear periodic structures III Nonsolitonic pulse pro...
Journal of the Optical Society of America B
April 2003
Stable vortex and dipole vector solitons in a saturable nonlinear medium
January 2003
Evans Function for the AKNS Problem with Algebraic Solitons
January 2003
Averaging of Dispersion-Managed Solitons: Existence and Stability
SIAM Journal on Applied Mathematics
January 2003
Depletion layer and contact capacitance in non-uniformly doped semiconductors
Journal of Physics D Applied Physics
November 2002
Semi-stability of embedded solitons in the general fifth-order KdV equation
Wave Motion
September 2002
Stable all-optical limiting in nonlinear periodic structures II Computations
Journal of the Optical Society of America B
August 2002
Generation of large-amplitude solitons in the extended Korteweg–de Vries equation
Chaos An Interdisciplinary Journal of Nonlinear Science
January 2002
Stable all-optical limiting in nonlinear periodic structures I Analysis
Journal of the Optical Society of America B
January 2002
Wave group dynamics in weakly nonlinear long-wave models
Physica D Nonlinear Phenomena
November 2001
Transverse Instability of Vector Solitons and Generation of Dipole Arrays
Physical Review Letters
August 2001
Interaction of lumps with a line soliton for the DSII equation
Physica D Nonlinear Phenomena
May 2001
A mysterious threshold for transverse instability of deep-water solitons
Mathematics and Computers in Simulation
March 2001
Stability criterion for multicomponent solitary waves
December 2000
Transmission regimes of periodic nonlinear optical structures
October 2000
Internal Oscillations and Radiation Damping of Vector Solitons
Studies in Applied Mathematics
October 2000
Instabilities of dispersion-managed solitons in the normal dispersion regime
September 2000
Self-focusing and transverse instabilities of solitary waves
Physics Reports
June 2000
OSCILLATORY INSTABILITY AND SUPERCRITICAL DYNAMICS OF DAMPED-DRIVEN NONLINEAR SCHRÖDING...
May 2000
Spectral decomposition for the Dirac system associated to the DSII equation
Inverse Problems
January 2000
Persistent oscillations of scalar and vector dispersion-managed solitons
Chaos An Interdisciplinary Journal of Nonlinear Science
January 2000
Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inver...
Communications in Mathematical Physics
January 2000
Asymptotic approximations for a new eigenvalue in linear problems without a threshold
Theoretical and Mathematical Physics
January 2000
Асимптотики нового собственного значения в линейных задачах без порога
Теоретическая и математическая физика
January 2000
Generation of soliton oscillations in nonlinear quadratic materials
June 1999
Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory ...
Nonlinearity
January 1999
Exact vortex solutions of the complex sine-Gordon theory on the plane
Physics Letters B
September 1998
Radiative effects to the adiabatic dynamics of envelope-wave solitons
Physica D Nonlinear Phenomena
August 1998
Internal Modes of Solitary Waves
Physical Review Letters
June 1998
Vibrations and Oscillatory Instabilities of Gap Solitons
Physical Review Letters
June 1998
Internal modes of envelope solitons
Physica D Nonlinear Phenomena
May 1998
On internal wave–shear flow resonance in shallow water
Journal of Fluid Mechanics
January 1998
Bifurcations of new eigenvalues for the Benjamin–Ono equation
Journal of Mathematical Physics
January 1998
Rational solutions of the KP hierarchy and the dynamics of their poles. II. Constructio...
Journal of Mathematical Physics
January 1998
On modified NLS, Kaup and NLBq equations: differential transformations and bilinearization
Journal of Physics A Mathematical and General
December 1997
Structural transformation of eigenvalues for a perturbed algebraic soliton potential
Physics Letters A
May 1997
Instability analysis of internal solitary waves in a nearly uniformly stratified fluid
Physics of Fluids
January 1997
An asymptotic approach to solitary wave instability and critical collapse in long-wave ...
Physica D Nonlinear Phenomena
November 1996
Instability-induced dynamics of dark solitons
August 1996
Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized n...
February 1996
GENERATION OF COLLECTIVE-ACTIVITY STRUCTURES IN A HOMOGENEOUS NEURON-LIKE MEDIUM I: BIF...
International Journal of Bifurcation and Chaos
January 1996
GENERATION OF COLLECTIVE-ACTIVITY STRUCTURES IN A HOMOGENEOUS NEURON-LIKE MEDIUM II: DY...
International Journal of Bifurcation and Chaos
January 1996
Nonlinear Theory of Soliton Instabilities
January 1996
On the asymptotic integrability of a higher-order evolution equation describing interna...
Journal of Mathematical Physics
January 1996
Collapse transformation for self-focusing solitary waves in boundary-layer type shear f...
Physics Letters A
October 1995
On a structure of the explicit solutions to the Davey-Stewartson equations
Physica D Nonlinear Phenomena
October 1995
Asymptotic theory of plane soliton self-focusing in two-dimensional wave media
Physica D Nonlinear Phenomena
August 1995
Instability of Solitons Governed by Quadratic Nonlinearities
Physical Review Letters
July 1995
On a wave field transformation described by the two-dimensional Kadomtsev-Petviashvili ...
Inverse Problems
June 1995
Self-focusing of plane dark solitons in nonlinear defocusing media
May 1995
Intermediate nonlinear Schrödinger equation for internal waves in a fluid of finite depth
Physics Letters A
February 1995
A spectral transform for the intermediate nonlinear Schrödinger equation
Journal of Mathematical Physics
January 1995
The structure of the rational solutions to the Boussinesq equation
Physica D Nonlinear Phenomena
January 1995
Instability and decay of solitary waves in the Davey-Stewartson 1 system
Physics Letters A
December 1994
Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their po...
Journal of Mathematical Physics
January 1994
Formation of pulsed sources in neuro-like media
Asymptotic Reductions of the Gross-Pitaevskii Equation
Nonlinear propagation of ultrashort pulses in nonlinear periodic materials with alterna...
A set of travelling fronts of excitation in the model of homogeneous neuro-like medium ...