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
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:
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Existence and stability of nonlinear waves
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Nonlinear dispersive equations on metric graphs
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Lattice dynamical systems and normal forms
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Justification of amplitude equations
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Analysis of integrable equations
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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: | ||||
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| Lynnyngs Kelly Arruda Saraiva de Paiva | 2023-2024 | Periodic waves in the modified KdV equation | Universidade Federal de Sao Carlos, Brazil |
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| Adilbek Kairzhan | 2020-2023 | Nonlinear waves on graph models | Nasarbaev University, Astana, Kazakhstan | 
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| 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 |
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| Hyungjin Huh | 2017-2019 | Nonlinear Dirac equations | Chung-Ang University, South Korea |
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| Jinbing Chen | 2016-2018 | Rogue periodic waves | SouthEast University, China |
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| 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 |
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| 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 |
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| 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 |
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| Nikolay Hristov | 2017-2021 | Amplitude equations for FPU lattices | Gale Partners Inc, Ontario |
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| Uyen Le | 2017-2021 | Stability of periodic waves | Lecturer, Vietnam |
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| Adilbek Kairzhan | 2016-2020 | Nonlinear waves on graph models | University of Toronto, Canada |
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| Alexander Chernyavsky | 2014-2018 | Stability of PT-symmetric lattices | University of Cape Town, South Africa |
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| 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 |
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| 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 |
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| Ana Mucalica | 2021-2023 | Solitons on dispersive shock waves | PhD, University of British Columbia |
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| Nabil Al Asmer | 2019-2021 | Bargmann transforms in PDEs | PhD, University of Calgary |
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| Algerim Madiyeva | 2019-2021 | Stability of peaked periodic waves | PhD, Nazarbaev University, Kazakhstan |
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| Robert White | 2018-2020 | Rogue waves on the periodic background | Eastern Charlotte Waterways (NB, Canada) |
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| Jin Li | 2015-2017 | Stability of periodic waves in KP-II equation | McGill University, Canada |
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| Amjad Khan | 2013-2015 | Approximations of lattice dynamics | University of Western Ontario, Canada |
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| 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 |
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| 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 |
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| Undergraduate students: | ||||
| Shuoyang Wang | 2024-2025 | Spectral stability of singular waves | McMaster University |
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| Spencer Locke | 2023-2024 | Stokes periodic waves in fluids | University of Michigan at Ann Arbor |
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| Jeanne Lin | 2022-2023 | Modeling of the modular Burgers equation | McMaster University |
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| Erin Redfearn | 2021-2022 | Multi-shocks in modular Burgers equation | McMaster University |
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| 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 |
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| Chengzhu Xu | 2012-2013 | Modeling of contact lines in fluid flows | University of Waterloo |
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| 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 |
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| 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 | |
| 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 | |