Research

My research interests include fluid mechanics, partial differential equations, computational mathematics and the associated numerical analysis, oceanography, coastal engineering and mathematical economics. Most of my research has been done with a collection of excellent collaborators whose identity can be ascertained in the complete list of publications.



2009 -- 2018

• (In collaboration with H. Chen & O. Karakashian) Finite element methods for a system of dispersive equations. (2018-3)
  
  
• (In collaboration with X. Carvajal, M. Panthee & M. Scialom) Higher order Hamiltonian model for unidirectional water waves. (2018-2)
  
  
• (In collaboration with S.-M. Sun & B.-Y. Zhang) Nonhomogeneous boundary-value problems for one dimensional nonlinear Schrödinger equations. (2018-1)
  
  
• (In collaboration with H. Chen & O. Karakashian) Stability of solitary-wave solutions of systems of dispersive equations. (2017-2)
  
  
• (In collaboration with M. Dai) Norm-inflation results for the BBM equation. (2017-1)
  
  
• (In collaboration with M. Chen) Singular solutions of a Boussinesq system for water waves. (2016-2)
  
  
• (In collaboration with A. Esfahani & A. Pastor) Stability and decay properties of solitary-wave solutions to the generalized BO-ZK equation.(2015-1)
  
  
• (In collaboration with J. Cohen & G. Wang) Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities. (2014-4)
  
  
• (In collaboration with G. Ponce, J.-C. Saut & C. Sparber) Dispersive blow-up for nonlinear Schrödinger equations revisited. (2014-3)
  
  
• (In collaboration with H. Chen & C.-H. Hsia) Well-posedness for the BBM-equation in a quarter plane. (2014-2)
  
  
• (In collaboration with D. Ambrose & D. Nicholls) On ill-posedness of truncated series models for water waves. (2014-1)
  
  
• (In collaboration with H. Chen) Periodic traveling-wave solutions of nonlinear dispersive evolution equations. (2013-4)
  
  
• (In collaboration with S. Vento & F. Weissler) Singularity formation and blowup of complex-valued soltuions of the modified KdV equation. (2013-3)
  
  
• (In collaboration with H. Chen, O. Karakashian & Y. Xing) Conservative, discontinuous Galerkin-methods for the generalized Korteweg-de Vries equation. (2013-2)
  
  
• (In collaboration with T. Colin & C. Guillope) Propagation of long-crested water waves. (2013-1)
  
  
• (In collaboration with D. Ambrose & D. Nicholls) Well-posedness of a model for water waves with viscosity. (2012-1)
  
  
• (In collaboration with Fred B. Weissler) Traveling fronts of a conservation law with hyper-dissipation (2011-5)
  
  
• (In collaboration with C.-H. Hsia, T. Ma & S. Wang) Hopf bifurcation for two-dimensional doubly diffusive convection. (2011-3)
  
  
• (In collaboration with L. Luo) Large-time asymptotics of the generalized Benjamin-Ono-Burgers equation. (2011-2)
  
  
• (In collaboration with J.-C. Saut) Dispersive blow-up II. Schrödinger equations, optical and oceanic rogue waves. (2010-4)
  
  
• (In collaboration with H. Chen, S.-M. Sun & B.-Y. Zhang) Approximating IVP by two-point BVP: The BBM equation. (2010-3)
  
  
• (In collaboration with D. Pilod) Stability of solitary-wave solutions to the Hironta-Satsuma equation. (2010-2)
  
  
• (In collaboration with Z. Grujic & H. Kalisch) A KdV-type Boussinesq system: from the energy level to analytic spaces. (2010-1)
  
  
• (In collaboration with S.-M. Sun & B.-Y. Zhang) A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain II. (2009-7)
  
  
• (In collaboration with H. Fathallah-Shaykh & S. Kadener) Mathematical model of the Drosophila circadian clock: loop and transcriptional integration. (2009-6)
  
  
• (In collaboration with F. Weissler) Pole dynamics of interacting solitons and blow-up of complex valued solutions of the KdV-equation. (2009-5)
  
  
• (In collaboration with H. Chen) Well-posedness for regularized nonlinear dispersive wave equations. (2009-4)
  
  
• (In collaboration with N. Tzvetkov) Sharp well-posedness results for the BBM equation. (2009-3)
  
  
• (In collaboration with J. Wu) Temporal growth and eventual periodicity for dispersive wave equations in a quarter plane. (2009-2)
  
  

Recent Collaborators

John Albert
Hongqiu Chen
Min Chen
Mimi Dai
Thierry Colin
Vassilios A. Dougalis
Hassan Fathallah-Shaykh
Thanasis Fokas
Zoran Grujic
Colette Guillope
Youngjoon Hong
Henryk Kalisch
Ohannes Karakashian
Barbara Karakiewicz
David Lannes
Jenny Li
Felipe Linares
Yue Liu
Dimitri Mitsotakis
David Nicholls
Jaime Angulo Pava
Gustavo Ponce
Juan Restrepo
Wojtek Romanczyk
Manuel Santos
Jean-Claude Saut
Marcia Scialom
Christof Sparber
Shuming Sun
Michael Tom
Nikolay Tzvetkov
Ed Thornton
Vladimir Varlamov
Ed Vrscay
Fred Weissler
Jiahong Wu
Bing-Yu Zhang

Related Links
AAAS
AMS
AWM
MAA
MER
SIAM