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
Pinning phenomenon for existence and stability of wave patterns 2024 G. Medvedev, L. Bengel, W. Reichel
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Traveling waves in the Babenko equation for water waves 2024 S. Locke
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Dispersive hydrodynamics in the modified KdV equation 2024 J. Chen, S. Cui, A. Mucalica, M. Hoefer, L. K. Arruda
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Instability of peaked waves in hydrodynamical models 2024 A. Geyer, F. Natali, S. Lafortune, S. Locke, Y. Liu
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Traveling waves in the Camassa–Holm equations: their stability and instability 2024 A. Geyer, F. Natali, S. Lafortune, Y. Liu
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Existence of breathers (modulating pulses) in periodic systems via spatial dynamics 2024 C. Chong, T. Dohnal, G. Schneider
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Domain walls with and without external potentials 2023 A. Contreras, M. Plum, V. Slastikov
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Instability of peaked traveling waves in the Camassa–Holm models 2023 A. Geyer, F. Natali, S. Lafortune
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Solitons and breathers on the periodic wave background 2023 M. Hoefer, A. Mucalica download download
Dynamics of shocks in the modular Burgers equation 2023 P. Poullet, B. de Rijk download download
Rogue waves arising on the periodic waves of the Ablowitz–Ladik equation 2023 J. Chen download
Justification of the KdV, KP-II, and Toda equations from the Fermi-Pasta-Ulam particle system 2023 G. Schneider download download
Solitary waves under intensity-dependent dispersion 2022 M. Plum, P. Kevrekidis, R. Ross download download
Periodic waves in discrete MKDV equation: modulational instability and rogue waves 2022 J. Chen download download
Periodic and double periodic waves in NLS: existence and stability 2022 J. Chen download download
Justification of the KP-II approximation in dynamics of two-dimensional FPU systems 2022 N. Hristov, G. Schneider
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Exponentially small splitting for heteroclinic and homoclinic orbits in lattice equations 2022 G. Alfimov
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Stability of smooth travelling waves and instability of peaked travelling waves in the Camassa–Holm models 2022 A. Geyer, F. Natali, S. Lafortune download download
Domain walls in harmonic potentials 2022 A. Contreras, V. Slastikov
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Stability of smooth and peaked periodic waves in the Camassa-Holm equation 2021 A. Geyer, F. Natali
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Ground states of the energy super-critical Gross-Pitaevskii equation with harmonic potential 2021 Piotr Bizon, Szymon Sobieszek download download
Variational characterization of periodic waves in the fractional KdV equation 2021 U. Le, F. Natali
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Solitary waves under intensity-dependent dispersion 2021 P. Kevrekidis, R. Ross download download
Instability of breathers and double periodic waves in NLS 2021 M. Haragus download
Rogue waves on the background of periodic solutions of the DNLS equation 2021 J. Chen, J. Upsal download
Existence and stability of Klein-Gordon breathers in the small-amplitude limit 2021 J. Cuevas, P. Kevrekidis, T. Penati, S. Paleari download
Standing waves on quantum graphs: variational methods and the period function 2020 A. Kairzhan, R. Marangell, D. Noja download
Periodic waves in integrable equations: modulation instability and rogue waves 2020 J. Chen, R. White
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Instability of peaked waves in the Camassa-Holm equation 2020 F. Natali, A. Madiyeva
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"Periodic waves in the fractional KdV equation" 2019 F. Natali, U.Le download
"Instability of peaked waves" 2019 A. Geyer, F. Natali download download
"Rogue waves on the periodic and double-periodic background" 2019 J. Chen, R. White download download
"Drift and instability of steady states" 2019 A. Kairzhan, R. Goodman download download
"Stationary states on metric graphs in the limit of large mass" 2018 G. Berkolaiko, J. Marzuola download
"Integrable semi-discretizations of integrable PDEs" 2018 N. Joshi 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
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"Stability of domain walls in coupled systems" 2017 S. Alama, L. Bronsard, A. Contreras, M. Plum download
"Ground state of the conformal flow on three-sphere" 2017 P. Bizon
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"Inverse scattering for the massive Thirring model" 2017 A. Saalmann, Y. Shimabukuro
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"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
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"Stability of nonlinear waves in integrable Hamiltonian PDEs" 2017
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"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

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"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
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"Well-posedness and stability in integrable systems" 2015 Y. Shimabukuro
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"Heteroclinic orbits for travelling kinks in difference and nonlocal wave equations" 2015 G.L. Alfimov
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"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
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"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
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"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
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"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
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"Validity of the weakly nonlinear solution for the Boussinesq-Ostrovsky equation" 2013 K. Khusnutdinova
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"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
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"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
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"Bifurcations of asymmetric vortices in symmetric harmonic potentials" 2012 P.G. Kevrekidis download download
"Enstrophy growth in the viscous Burgers equation" 2012

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"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
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"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
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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 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
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"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
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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 download
"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 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
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"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
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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 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

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"Evans function for Lax operators with algebraic potentials" 2005 M. Klaus download
"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 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
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"Parametric resonance and radiative decay of dispersion-managed solitons" 2003 V. Zharnitsky,
J. Yang
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