Research Group

My research group works in the areas of nonlinear partial differential equations, lattice differential equations, integrable systems, nonlinear waves, and mathematical modeling in physical problems. More specifically, we work on the following three fundamental themes:

Existence and stability of nonlinear waves
Nonlinear dispersive equations on metric graphs
Lattice dynamical systems and normal forms
Justification of amplitude equations
Analysis of integrable equations

We are a part of the AIMS Laboratory at Deparment of Mathematics at McMaster University. Current and former postdoctoral, graduate and undergraduate members of my research team include the following trainees:

Research fellows:
Lynnyngs Kelly Arruda Saraiva de Paiva 2023-2024 Periodic waves in the modified KdV equation Universidade Federal de Sao Carlos, Brazil
Adilbek Kairzhan 2020-2023 Nonlinear waves on graph models Nasarbaev University, Astana, Kazakhstan download download
Tao Xu 2018-2020 Integrable semi-discretization China University of Petroleum-Beijing download
Fabio Natali 2018-2020 Stability of periodic waves State University of Maringa, Brazil download download download download
Hyungjin Huh 2017-2019 Nonlinear Dirac equations Chung-Ang University, South Korea download download
Jinbing Chen 2016-2018 Rogue periodic waves SouthEast University, China download download download download download download download
Hichem Hajaiej 2016-2017 Logarithmic NLS equation UCalifornia State University, USA
Jamie Foster 2014-2016 Interfaces in slow diffusion systems University of Portsmouth, England download download
Gaukhar Shaikhova 2014-2015 Stationary NLS equation on graphs University of Astana, Kazakhstan download
Andres Contreras 2012-2014 Stability of solitary waves New Mexico State University, USA download download download download download
Wei Alan Zhao 2010-2012 Mathematical modeling of drug delivery Manulife Financial download
Juan Belmonte-Beitia 2009-2010 Gross-Pitaevskii equation with sign-varying nonlinearity University of Castilla-La Mancha, Spain download
Clement Gallo 2007-2009 Nonlinear waves in Bose-Einstein condensates University of Montpellier, France download download download
Ranis Ibragimov 2005-2007 Navier-Stokes equations and fluid dynamics New Mexico Institute of Mining and Technology, New Mexico, USA download download download
Vitaly Vougalter 2002-2004 Spectral stability of NLS solitons University of Notre-Dame, USA download download
Henrik Kalisch 2001-2002 Numerical modeling of dispersion management University of Bergen, Norway download
Ph.D. students:
James Hornick 2023-2027 Nonlinear waves in dynamics of fluids

Szymon Sobieszek 2019-2023 Bound states in Gross-Pitaevskii theory
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Nikolay Hristov 2017-2021 Amplitude equations for FPU lattices Gale Partners Inc, Ontario download download download
Uyen Le 2017-2021 Stability of periodic waves Lecturer, Vietnam download download download download download download download download
Adilbek Kairzhan 2016-2020 Nonlinear waves on graph models University of Toronto, Canada download download download download download
Alexander Chernyavsky 2014-2018 Stability of PT-symmetric lattices University of Cape Town, South Africa download download download download download
Yusuke Shimabukuro 2012-2016 Analysis of integrable PDEs Institute of Mathematics, Taipei, Taiwan download download download download download download
Anton Sakovich 2009-2013 Nonlinear waves in weakly-coupled lattices MicroMetrics, Ottawa download download download download
Marina Chugunova 2004-2007 Spectral stability of nonlinear waves in dynamical systems University of Toronto, Canada download download download download download download download download download
M.Sc. students:
Jiaqi Han 2023-2025 Algebraic solitons in the massive Thirring model

Al-Tarazi Assaubay 2021-2023 Completeness of eigenfunctions in NLS Lecturer, Nazarbaev University, Kazakhstan download download
Ana Mucalica 2021-2023 Solitons on dispersive shock waves PhD, University of British Columbia download download download download
Nabil Al Asmer 2019-2021 Bargmann transforms in PDEs PhD, University of Calgary download download
Algerim Madiyeva 2019-2021 Stability of peaked periodic waves PhD, Nazarbaev University, Kazakhstan download download download
Robert White 2018-2020 Rogue waves on the periodic background Eastern Charlotte Waterways (NB, Canada) download download download download download
Jin Li 2015-2017 Stability of periodic waves in KP-II equation McGill University, Canada download download
Amjad Khan 2013-2015 Approximations of lattice dynamics University of Western Ontario, Canada download download download
Mostafa Abdi 2011-2012 Approximations of vortices in the Gross-Pitaevskii equation McMaster University download download
Matthew Betti 2010-2012 Periodic travelling waves in diatomic granular crystals University of Western Ontario download download download
Dmitry Ponomarev 2010-2012 Justification of the nonlinear Schrodinger equation for polymers University of Nice, France downloaddownload
Anton Sakovich 2007-2009 Pulse solutions of nonlinear dispersive equations McMaster University download download download download
Ahmed Hassan Abdelrazec 2007-2009 Convergence of the Adomian decomposition method York University, Canada download download
Dmitri Agueev 2002-2004 Well-posedness of coupled-mode equations McMaster University download download
Clayton Webster 2001-2003 Numerical modelling of waveguide interfaces Florida State University download download
Undergraduate students:
Shuoyang Wang 2024-2025 Spectral stability of singular waves McMaster University
Spencer Locke 2023-2024 Stokes periodic waves in fluids University of Michigan at Ann Arbor
Jeanne Lin 2022-2023 Modeling of the modular Burgers equation McMaster University download
Erin Redfearn 2021-2022 Multi-shocks in modular Burgers equation McMaster University
Kevin Xiao 2019-2020 Energy minimization on flower graph McGill University download
Swaleh Hussain 2019-2020 Discrete Chern-Simons-Schrodinger theory McMaster University download
Leeor Greenblat 2018-2019 Integrable semi-discretization of MTM system McMaster University download
Michael Chong 2016-2017 Chaotic sets in Lorentz systems McMaster University download
Sylvie Bronsard 2016-2017 Integrable discretizations of DNLS equations Courant Institute, USA download
Peter Gysberg 2015-2016 Reversing interfaces under slow diffusion and strong absorption University of British Columbia download download
Chengzhu Xu 2012-2013 Modeling of contact lines in fluid flows University of Waterloo download download download
James Dowdall 2012-2013 Symmetry-breaking bifurcations in PT-symmetric systems University of Ottawa
Mathew Coles 2010-2011 Bifurcations of Bloch waves University of British Columbia download download download
Daniel Badali
Alex Kulik
Steven Pollack
2010-2011 Bifurcation analysis of steady states in rimming flows with surface tension University of Toronto
Kharkov Technical University
McGill University
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James Brown, B.Sc. 2009-2010 Numerical approximations of localized modes in periodic potentials Queen's University download download download
Mathew Coles, B.Sc. 2009-2010 Excited states in Bose-Einstein condensates McMaster University download
Peter Foltin, B.Sc. 2008-2009 Propagation failure in nonlinear lattices University of Toronto
Mike Lukas, B.Sc. 2006-2007 Symbolic computing of discrete 3D vortices University of Toronto download
Marcella Fioroni, B.Sc. 2005-2006 Iterative methods for bound states York University
Yourik Hacoupian, B.Sc. 2002-2003 Software development in photonic optics McMaster University
Guanrong Lou, B.Sc.
Le Bing, B.Sc.
2001-2002 Software development for web simulations McMaster University
Exchange students:
Cheng He, Ph.D Mathematics 2024-2025 Analysis of the massive Thirring model Ningbo University, China
Aaron Saalmann, Ph.D Mathematics, Cologne 2016-2017 Analysis of integrable PDEs University of Cologne, Germany download download
Jamin Sheriff, M.Sc.
2002-2003 Modelling of 3D nonlinear photonic crystals University of Toronto, Canada download
Joyce Poon, B.Sc.
2001-2002 Asymptotic methods for photonic waveguides Caltech, USA download
Winnie Ye, M.Sc.
2001-2002 Numerical modeling of coupled-mode equations NRC-CNRC, Canada download
Lukasz Brzozowski, Ph.D.
2000-2003 Coupled-mode equations in photonic optics Novadaq Technologies Inc, Canada download