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:
Stefan Le Coz	2024-2025	Traveling waves on the periodic metric graphs	University of Toulouse, France
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
Tao Xu	2018-2020	Integrable semi-discretization	China University of Petroleum-Beijing
Fabio Natali	2018-2020	Stability of periodic waves	State University of Maringa, Brazil
Hyungjin Huh	2017-2019	Nonlinear Dirac equations	Chung-Ang University, South Korea
Jinbing Chen	2016-2018	Rogue periodic waves	SouthEast University, China
Hichem Hajaiej	2016-2017	Logarithmic NLS equation	UCalifornia State University, USA
Jamie Foster	2014-2016	Interfaces in slow diffusion systems	University of Portsmouth, England
Gaukhar Shaikhova	2014-2015	Stationary NLS equation on graphs	University of Astana, Kazakhstan
Andres Contreras	2012-2014	Stability of solitary waves	New Mexico State University, USA
Wei Alan Zhao	2010-2012	Mathematical modeling of drug delivery	Manulife Financial
Juan Belmonte-Beitia	2009-2010	Gross-Pitaevskii equation with sign-varying nonlinearity	University of Castilla-La Mancha, Spain
Clement Gallo	2007-2009	Nonlinear waves in Bose-Einstein condensates	University of Montpellier, France
Ranis Ibragimov	2005-2007	Navier-Stokes equations and fluid dynamics	New Mexico Institute of Mining and Technology, New Mexico, USA
Vitaly Vougalter	2002-2004	Spectral stability of NLS solitons	University of Notre-Dame, USA
Henrik Kalisch	2001-2002	Numerical modeling of dispersion management	University of Bergen, Norway
Ph.D. students:
James Hornick	2023-2027	Nonlinear waves in dynamics of fluids
Szymon Sobieszek	2019-2023	Bound states in Gross-Pitaevskii theory
Nikolay Hristov	2017-2021	Amplitude equations for FPU lattices	Gale Partners Inc, Ontario
Uyen Le	2017-2021	Stability of periodic waves	Lecturer, Vietnam
Adilbek Kairzhan	2016-2020	Nonlinear waves on graph models	University of Toronto, Canada
Alexander Chernyavsky	2014-2018	Stability of PT-symmetric lattices	University of Cape Town, South Africa
Yusuke Shimabukuro	2012-2016	Analysis of integrable PDEs	Institute of Mathematics, Taipei, Taiwan
Anton Sakovich	2009-2013	Nonlinear waves in weakly-coupled lattices	MicroMetrics, Ottawa
Marina Chugunova	2004-2007	Spectral stability of nonlinear waves in dynamical systems	University of Toronto, Canada
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
Ana Mucalica	2021-2023	Solitons on dispersive shock waves	PhD, University of British Columbia
Nabil Al Asmer	2019-2021	Bargmann transforms in PDEs	PhD, University of Calgary
Algerim Madiyeva	2019-2021	Stability of peaked periodic waves	PhD, Nazarbaev University, Kazakhstan
Robert White	2018-2020	Rogue waves on the periodic background	Eastern Charlotte Waterways (NB, Canada)
Jin Li	2015-2017	Stability of periodic waves in KP-II equation	McGill University, Canada
Amjad Khan	2013-2015	Approximations of lattice dynamics	University of Western Ontario, Canada
Mostafa Abdi	2011-2012	Approximations of vortices in the Gross-Pitaevskii equation	McMaster University
Matthew Betti	2010-2012	Periodic travelling waves in diatomic granular crystals	University of Western Ontario
Dmitry Ponomarev	2010-2012	Justification of the nonlinear Schrodinger equation for polymers	University of Nice, France
Anton Sakovich	2007-2009	Pulse solutions of nonlinear dispersive equations	McMaster University
Ahmed Hassan Abdelrazec	2007-2009	Convergence of the Adomian decomposition method	York University, Canada
Dmitri Agueev	2002-2004	Well-posedness of coupled-mode equations	McMaster University
Clayton Webster	2001-2003	Numerical modelling of waveguide interfaces	Florida State University
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
Erin Redfearn	2021-2022	Multi-shocks in modular Burgers equation	McMaster University
Kevin Xiao	2019-2020	Energy minimization on flower graph	McGill University
Swaleh Hussain	2019-2020	Discrete Chern-Simons-Schrodinger theory	McMaster University
Leeor Greenblat	2018-2019	Integrable semi-discretization of MTM system	McMaster University
Michael Chong	2016-2017	Chaotic sets in Lorentz systems	McMaster University
Sylvie Bronsard	2016-2017	Integrable discretizations of DNLS equations	Courant Institute, USA
Peter Gysberg	2015-2016	Reversing interfaces under slow diffusion and strong absorption	University of British Columbia
Chengzhu Xu	2012-2013	Modeling of contact lines in fluid flows	University of Waterloo
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
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
James Brown, B.Sc.	2009-2010	Numerical approximations of localized modes in periodic potentials	Queen's University
Mathew Coles, B.Sc.	2009-2010	Excited states in Bose-Einstein condensates	McMaster University
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
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
Shikun Cui, Ph.D Mathematics	2024-2025	Stability of traveling periodic waves in integrable systems	Dalian University of Technology, China
Zhi-Qiang Li, Ph.D Mathematics	2024-2025	Double eigenvalues in IST for massive Thirring model	University of Mining and Technology, Xuzhou, China
Aaron Saalmann, Ph.D Mathematics, Cologne	2016-2017	Analysis of integrable PDEs	University of Cologne, Germany
Jamin Sheriff, M.Sc. ECE, UofT	2002-2003	Modelling of 3D nonlinear photonic crystals	University of Toronto, Canada
Joyce Poon, B.Sc. ECE, UofT	2001-2002	Asymptotic methods for photonic waveguides	Caltech, USA
Winnie Ye, M.Sc. ECE, UofT	2001-2002	Numerical modeling of coupled-mode equations	NRC-CNRC, Canada
Lukasz Brzozowski, Ph.D. ECE, UofT	2000-2003	Coupled-mode equations in photonic optics	Novadaq Technologies Inc, Canada