Research Presentations

My main research interests are in existence, stability, and global dynamics of nonlinear waves in dispersive wave equations, lattice differential equations, and diffusion-advection equations. These topics involve aplied harmonic analysis, PDE theory, spectral analysis, dynamical systems, asymptotic analysis, numerical methods. Slides of presentations at conferences and seminars are available in the reverse chronological order.

Title Year Coauthors Conference Lecture
"Integrable semi-discretizations of integrable PDEs" 2018 N. Joshi download
"Stationary states on metric graphs in the limit of large mass" 2018 G. Berkolaiko, J. Marzuola download
"Krein signature in PT-symmetric systems" 2018 A. Chernyavsky download
"Instability of peaked periodic waves in reduced Ostrovsky equations" 2018 A. Geyer download download
"Rogue waves on the periodic background" 2018 J. Chen download download
"Bifurcations of self-similar solutions for reversing interface" 2018 J. Foster
"Stability of domain walls in coupled systems" 2017 S. Alama, L. Bronsard, A. Contreras download
"Ground state of the conformal flow on three-sphere" 2017 P. Bizon
"Inverse scattering for the massive Thirring model" 2017 A. Saalmann, Y. Shimabukuro
"Nonlinear instability of half-solitons on star graphs" 2017 A. Kairzhan download download
"Bifurcations of multi-vortex configurations in rotating BECs" 2017 C. Garcia-Azpeitia
"Stability of nonlinear waves in integrable Hamiltonian PDEs" 2017
download download
"Transverse stability of periodic waves in KP-II" 2017 M. Haragus download
"Spectral stability of periodic waves in reduced Ostrovsky equations" 2017 E.Johnson, A. Geyer download
"Logarithmic Korteweg-De Vries equation" 2017

"Self-similar solutions for reversing interface in the slow diffusion equation" 2016 J. Foster download download
"Stability of breathers in nonlinear lattices" 2016 J. Cuevas and P. Kevrekidis download download
"Nonlinear Schrodinger equation on the periodic graph" 2016 G. Schneider download download download download download
"Ground states on the bounded and unbounded graphs" 2016 J. Marzuola download download
"Hamiltonian PT-symmetric chains of coupled pendula" 2016 A. Chernyavsky
"Well-posedness and stability in integrable systems" 2015 Y. Shimabukuro
"Heteroclinic orbits for travelling kinks in difference and nonlocal wave equations" 2015 G.L. Alfimov
"Approximations of dynamics of nonlinear lattices on the extended time scale" 2015 A. Khan, T. Penati, S. Paleari download
"Global solutions and wave breaking in the reduced Ostrovsky equation" 2015 R. Grimshaw
"Existence and stability of standing waves of the NLS equation on the tadpole graph" 2015 D. Noja, G. Shaikhova download download
"Stability of Dirac solitons" 2015 Y. Shimabukuro
"Stability of periodic waves and black solitons in the cubic defocusing NLS equation" 2014 Th. Gallay download
"Nonlinear dynamics in PT-symmetric lattices" 2014 P. Kevrekidis
V. Konotop
I. Barashenkov
"Thomas-Fermi ground state in a PT-symmetric confining potential" 2014 C. Gallo download
"Justification of the log-KdV equation for granular chains" 2014 E. Dumas download
"Orbital stability of Gaussian solitons in the log-KdV equation" 2014 R. Carles download download
"Orbital stability of Dirac (MTM) solitons" 2013 Y. Shimabukuro
"Validity of the weakly nonlinear solution for the Boussinesq-Ostrovsky equation" 2013 K. Khusnutdinova
"Gaussian solitary waves in granular crystals" 2013 G. James download download
"Bifurcations and resonance of breathers in the discrete Klein-Gordon equation" 2013 A.Sakovich download download
"Spectral stability of nonlinear waves in KdV equations" 2013
download download
"Nonlinear states in PT-symmetric lattices" 2013 P. Kevrekidis download download
"On transverse stability of discrete solitons" 2012 J. Yang download download
"Periodic travelling waves in diatomic granular chains" 2012 M. Betti download download
"Variational approximations in discrete nonlinear Schrodinger equations" 2012 C. Chong
"Bifurcations of asymmetric vortices in symmetric harmonic potentials" 2012 P.G. Kevrekidis download download
"Enstrophy growth in the viscous Burgers equation" 2012

"Justification of the short-pulse equation" 2011 G. Schneider download download
"Nonlinear Dirac equations in one spatial dimension" 2011 A. Stefanov download download
"Polychromatic solitary waves in the periodic nonlinear Maxwell equations" 2011 G. Simpson, M. Weinstein download download
"Propagation failure in the discrete Nagumo equation" 2011 H.J. Hupkes, B. Sandstede download
"Multi-site breathers in Klein-Gordon lattices: bifurcations, stability, and resonances" 2011 A.Sakovich download
"Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation" 2011 A.Sakovich download
"Backlund transformation and L2-stability of NLS solitons" 2011 T. Mizumachi download download
"Wave breaking in the Ostrovsky-Hunter equation" 2010 Y. Liu
A. Sakovich
download download
"Vortices in a harmonic potential" 2010 P. Kevrekidis download download
"Excited states in a harmonic potential" 2010 P. Kevrekidis download download
"Symmetry-breaking bifurcations in a double-well potential" 2010 E. Kirr, P. Kevrekidis
"Global well-posedness and wave breaking in the short-pulse equation" 2010 Y. Liu
A. Sakovich
download download
"Breathers from infinity in the anti-continuum limit" 2009 G. James
"Justification of the DNLS equation for sign-varying nonlinearities" 2009 J. Belmonte-Beitia download
"Ground states in a harmonic potential" 2009 C. Gallo download
"Asymptotic stability of discrete solitons" 2009 A. Stefanov download download
"Spectrum of an advection-diffusion operator" 2008 M.Chugunova download download
"Localized modes in NLS lattices" 2008 P. Panayotaros, A. Stefanov
"Eigenvalues of nonlinear ground state in the Thomas-Fermi approximation" 2008 C. Gallo download
"Justification of tight-binding approximation in nonlinear Schrodinger lattices" 2008 R. MacKay
G. Schneider
download download
"Localized traveling waves in nonlinear Schrodinger lattices" 2007 T. Melvin
A. Champneys
"Hamiltonian lattice for nonlinear waves with parabolic potentials" 2007 P. Kevrekidis download
"Coupled-mode equations and gap solitons in two dimensions" 2007 T. Dohnal,
G. Schneider
"Moving gap solitons in periodic potentials" 2007 G. Schneider download download
"Justification of coupled-mode equations for gap solitons" 2007 G. Schneider download download
"Dark solitons in external potentials" 2007 P. Kevrekidis download download
"Stability of incompressible viscous fluid flows in a spherical shell" 2007 R. Ibragimov download download
"Translationally invariant discrete NLS equation" 2006
"Transverse instabilities of deep-water solitary waves" 2006 B. Deconinck download download
"Multi-component vortices in coupled NLS equations" 2006 A. Desyatnikov download
"Two-pulse solutions in fifth-order KdV equation" 2006 M. Chugunova download download
"Nonlinearity management in time-periodic NLS systems" 2006 P. Kevrekidis,
V. Zharnitsky
download download
"Moving kink in discrete phi-4 models" 2005 O. Oxtoby,
I. Barashenkov
download download
"Photonic crystals, coupled-mode equations and gap solitons" 2005 D. Agueev
M. Chugunova
download download download
"Existence and stability of dark solitons in external potentials" 2005 D. Franzeskakis download download
"Persistence and stability of discrete vortices in NLS lattices" 2005 P. Kevrekidis download download
"Spectrum of the linearized NLS problem" 2005 S. Cuccagna,
V. Vougalter

"Evans function for Lax operators with algebraic potentials" 2005 M. Klaus download
"Iteration method for nonlinear wave equations" 2004 Yu. Stepanyants
"Solitons and vortices in discrete NLS equations" 2004 P. Kevrekidis
"Spectrum of embedded solitons in the third-order NLS equation" 2004 J. Yang download
"Bifurcations of travelling wave solutions in discrete NLS equations" 2004 V. Rothos download
"Spectral stability of KdV solitons" 2004 Yu. Kodama download
"Bifurcations of gap solitons in periodic potentials" 2003 A. Sukhorukov,
Yu. Kivshar
"Parametric resonance and radiative decay of dispersion-managed solitons" 2003 V. Zharnitsky,
J. Yang