My main research interests are in existence, stability, and nonlinear dynamics of solitary waves (solitons) in nonlinear wave equations and lattices. These topics involve PDE theory, spectral analysis, dynamical systems, asymptotic analysis, numerical methods, and functional analysis. Slides of presentations at conferences and seminars are available in the reverse chronological order.
| Title of the research project | Year | Coauthors | Conference | Seminar |
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| "Bifurcations of asymmetric vortices in symmetric harmonic potentials" | 2012 | P.G. Kevrekidis |
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| "Enstrophy growth in the viscous Burgers equation" | 2012 |
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| "Justification of the short-pulse equation" | 2011 | G. Schneider |
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| "Nonlinear Dirac equations in one spatial dimension" | 2011 | A. Stefanov |
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| "Broad band solitons in the periodic nonlinear Maxwell equations" | 2011 | G. Simpson, M. Weinstein |
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| "Propagation failure in the discrete Nagumo equation" | 2011 | H.J. Hupkes, B. Sandstede |
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| "Multi-site breathers in Klein-Gordon lattices: bifurcations, stability, and resonances" | 2011 | A.Sakovich |
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| "Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation" | 2011 | A.Sakovich |
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| "Backlund transformation and L2-stability of NLS solitons" | 2011 | T. Mizumachi |
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| "Wave breaking in the Ostrovsky–Hunter equation" | 2010 |
Y. Liu A. Sakovich |
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| "Vortices in a harmonic potential" | 2010 | P. Kevrekidis |
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| "Excited states in a harmonic potential" | 2010 | P. Kevrekidis |
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| "Symmetry-breaking bifurcations in a double-well potential" | 2010 | E. Kirr, P. Kevrekidis |
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| "Global well-posedness and wave breaking in the short-pulse equation" | 2010 |
Y. Liu A. Sakovich |
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| "Breathers from infinity in the anti-continuum limit" | 2009 | G. James |
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| "Justification of the DNLS equation for sign-varying nonlinearities" | 2009 | J. Belmonte-Beitia |
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| "Ground states in a harmonic potential" | 2009 | C. Gallo |
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| "Asymptotic stability of discrete solitons" | 2009 | A. Stefanov |
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| "Spectrum of an advection-diffusion operator" | 2008 | M.Chugunova |
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| "Localized modes in NLS lattices" | 2008 | P. Panayotaros, A. Stefanov |
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| "Eigenvalues of nonlinear ground state in the Thomas-Fermi approximation" | 2008 | C. Gallo |
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| "Justification of tight-binding approximation in nonlinear Schrodinger lattices" | 2008 |
R. MacKay G. Schneider |
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| "Localized traveling waves in nonlinear Schrodinger lattices" | 2007 |
T. Melvin A. Champneys |
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| "Hamiltonian lattice for nonlinear waves with parabolic potentials" | 2007 | P. Kevrekidis |
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| "Coupled-mode equations and gap solitons in two dimensions" | 2007 |
T. Dohnal, G. Schneider |
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| "Moving gap solitons in periodic potentials" | 2007 | G. Schneider |
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| "Justification of coupled-mode equations for gap solitons" | 2007 | G. Schneider |
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| "Dark solitons in external potentials" | 2007 | P. Kevrekidis |
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| "Stability of incompressible viscous fluid flows in a spherical shell" | 2007 | R. Ibragimov |
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| "Translationally invariant discrete NLS equation" | 2006 |
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| "Transverse instabilities of deep-water solitary waves" | 2006 | B. Deconinck |
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| "Multi-component vortices in coupled NLS equations" | 2006 | A. Desyatnikov |
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| "Two-pulse solutions in fifth-order KdV equation" | 2006 | M. Chugunova |
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| "Nonlinearity management in time-periodic NLS systems" | 2006 |
P. Kevrekidis, V. Zharnitsky |
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| "Moving kink in discrete phi-4 models" | 2005 |
O. Oxtoby, I. Barashenkov |
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| "Photonic crystals, coupled-mode equations and gap solitons" | 2005 |
D. Agueev M. Chugunova |
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| "Existence and stability of dark solitons in external potentials" | 2005 | D. Franzeskakis |
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| "Persistence and stability of discrete vortices in NLS lattices" | 2005 | P. Kevrekidis |
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| "Spectrum of the linearized NLS problem" | 2005 |
S. Cuccagna, V. Vougalter |
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| "Evans function for Lax operators with algebraic potentials" | 2005 | M. Klaus |
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| "Iteration method for nonlinear wave equations" | 2004 | Yu. Stepanyants |
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| "Solitons and vortices in discrete NLS equations" | 2004 | P. Kevrekidis |
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| "Spectrum of embedded solitons in the third-order NLS equation" | 2004 | J. Yang |
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| "Bifurcations of travelling wave solutions in discrete NLS equations" | 2004 | V. Rothos |
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| "Spectral stability of KdV solitons" | 2004 | Yu. Kodama |
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| "Bifurcations of gap solitons in periodic potentials" | 2003 |
A. Sukhorukov, Yu. Kivshar |
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| "Parametric resonance and radiative decay of dispersion-managed solitons" | 2003 |
V. Zharnitsky, J. Yang |
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For other information about my research activities, see