Research Group

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

Existence and stability of nonlinear waves
Analysis of nonlinear dispersive equations
Analysis of lattice dynamical systems

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:


Name Period Subject Moved to Outcomes
Postdoctoral fellows:
Jinbing Chen 2016-2017 Rogue waves in the modified KdV equation SouthEast University, China download
Hichem Hajaiej 2016-2017 Analysis of the log-NLS equation University of Tunis, Tunis
Jamie Foster 2014-2016 Interfaces in slow diffusion systems Portsmouth, England download
Gaukhar Shaikhova 2014-2015 Stationary NLS equation on graphs University of Astana, Kazahstan download
Andres Contreras 2012-2014 Stability of solitary waves University of New Mexico 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
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:
Adilbek Kairzhan 2016-2020 Nonlinear waves on graph models
download
Alexander Chernyavsky 2014-2018 Stability of PT-symmetric lattices
download download
Yusuke Shimabukuro 2012-2016 Analysis of integrable PDEs Institute of Mathematics, Taipei, Taiwan 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
M.Sc. students:
Jin Li 2015-2017 Stability of periodic waves in KP-II equation
download download
Amjad Khan 2013-2015 Approximations of lattice dynamics University of Western Ontario, Canada download download download
Kivilcim Alcan 2013-2014 Integrable flows University of Ankara, Turkey
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:
Michael Chong 2016-2017 Chaotic sets in Lorentz systems McMaster University download
Sylvie Bronsard 2016-2017 Integrable discretizations of DNLS equations McMaster University download
Peter Gysberg 2015-2016 Reversing interfaces under slow diffusion and strong absorption McMaster University 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
download download
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:
Aaron Saalmann 2016-2017 Analysis of integrable PDEs University of Cologne, Germany download
Jamin Sheriff, M.Sc.
jointly with ECE, UofT
2002-2003 Modelling of 3D nonlinear photonic crystals University of Toronto, Canada download
Joyce Poon, B.Sc.
jointly with ECE, UofT
2001-2002 Asymptotic methods for photonic waveguides Caltech, USA download
Winnie Ye, M.Sc.
jointly with ECE, UofT
2001-2002 Numerical modeling of coupled-mode equations NRC-CNRC, Canada download
Lukasz Brzozowski, Ph.D.
jointly with ECE, UofT
2000-2003 Coupled-mode equations in photonic optics Novadaq Technologies Inc, Canada download

Our current research themes include high-impact, applied and fundamental problems:

Stationary and traveling nonlinear waves in lattices
Well-posedness analysis of nonlinear evolution equations
Localized solutions in space-periodic and confining potentials
Partial differential equations with time-periodic coefficients
Spectral and asymptotic stability of nonlinear waves
Nonlinear waves in Burgers and Navier-Stokes equations

New projects will be developed in the next few years. To join our group, express your interest by e-mail.