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.



1989 -- 1998

• (In collaboration with M. Chen) A Boussinesq system for two-way propagation of nonlinear dispersive waves (1998-3)
  
  
• (In collaboration with H. Chen) Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations (1998-1)
  
  
• (In collaboration with Y.A. Li) Decay and analyticity of solitary waves (1997-4)
  
  
• (In collaboration with J.P. Albert & J.-C. Saut) Model equations for waves in stratified fluids (1997-3)
  
  
• (In collaboration with M.S. Santos) On the role of computation in economic theory (1997-1)
  
  
• (In collaboration with V.A. Dougalis,O.A. Karakashian & W.R. McKinney) The effect of dissipation on solutions of the generalized Korteweg-de Vries (1996-6)
  
  
• (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Numerical simulation of singular solutions of the generalized Korteweg-de Vries equation. (1996-4)
  
  
• (In collaboration with B.-Yu Zhang) The initial-value problem for the forced Korteweg-de Vries equation. (1996-3)
  
  
• (In collaboration with Y.A. Li) Analyticity of solitary-wave solutions of model equations for long waves. (1996-2)
  
  
• (In collaboration with H.A. Biagioni, R.J. Iorio Jr. & M. Scialom) On the Korteweg-de Vries-Kuramoto-Sivashinsky equation. (1996-1)
  
  
• (In collaboration with M. Scialom) On the comparisobn of solutions of model equations for long waves (1995-9)
  
  
• (In collaboration with K.S. Promislow & C.E. Wayne) Higher-order asymptotics of decaying solutions of some nonlinear, dispersive, dissipative wave equations. (1995-8)
  
  
• (In collaboration with J.M. Restrepo) Discretization of a model for the formation of longshore sand ridges. (1995-7)
  
  
• (In collaboration with M. Scialom) The effect of change in the nonlinearity and the dispersion relation of model equations for long waves. (1995-6)
  
  
• (In collaboration with J.M. Restrepo) Three dimensional model for the formation of longshore sand structures on the continental shelf. (1995-5)
  
  
• (In collaboration with L. Luo) More results on the decay of solutions to nonlinear, dispersive wave equations (1995-4)
  
  
• (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation. (1995-3)
  
  
• (In collaboration with L. Luo) Initial-boundary value problems for model equations for the propagation of long waves (1995-1)
  
  
• (In collaboration with K. Promislow & G. Wayne) On the asymptotic behavior of solutions to nonlinear, dispersive, dissipative wave equations (1994-5)
  
  
• (In collaboration with S.V. Rajopadhye & M.E. Schonbek) Models for propagation of bores I: Two dimensional theory (1994-1)
  
  
• (In collaboration with A. Soyeur) On the stability of solitary-wave solutions of model equations of Long Waves (1994-3)
  
  
• (In collaboration with L. Luo) Decay of solutions to nonlinear dispersive wave equations. (1993-4)
  
  
• (In collaboration with J.-C. Saut) Dispersive blowup of solutions of the generalized Korteweg-de Vries equations (1993-2)
  
  
• (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Numerical solution of the generalized Korteweg-de Vries-Burgers equation with adaptive Galerkin methods (1992-7)
  
  
• (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Computations for blow-up and decay for periodic solutions of the generalized Korteweg-de Vries-Burgers equation (1992-6)
  
  
• (In collaboration with F. Abergel) A mathematical theory for viscous, free-surface flows over a perturbed plane (1992-5)
  
  
• (In collaboration with G. Ponce, J.-C. Saut & M.M. Tom) A model system for strong interaction between internal solitary waves (1992-4)
  
  
• (In collaboration with the committee on the undergraduate program in mathematics) Undergraduate Major in the mathematical sciences. (1992-2)
  
  
• (In collaboration with R. Nelson) Relative size and comparative value in Byzantine illuminated manuscripts: some quantitative perspectives. (1992-1)
  
  
• (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. Mckinney) Fully-discrete methods with grid refinement for the generalized Korteweg-de Vries equation (1991-5)
  
  
• (In collaboration with B. Boczar-Karakiewicz & B. Pelchat) Interaction of internal waves with the seabed continental shelves (1991-4)
  
  
• (In collaboration with J.P. Albert) Comparisons between Model Equations for Long Waves (1991-3)
  
  
• (In collaboration with J.P. Albert) Total positivity and the stability of internal waves in stratified fluids of finite depth (1991-1)
  
  
• (In collaboration with T.B. Benjamin & D.K. Bose) Solitary-wave solutions of nonlinear problems (1990-1)
  
  
• (In collaboration with L. Abdelouhab, M. Felland & J.-C. Saut)Nonlocal Models for nonlinear dispersive waves (1989-7)
  
  
• (In collaboration with R.L. Sachs) The existence of internal solitary waves in a two-fluid system near the KdV limit (1989-6)
  
  
• (In collaboration with M.S. Santos) On the structure of the equilibrium set of overlapping-generations economies. (1989-5)
  
  
• (In collaboration with C.J. Amick & M.E. Schonbek)Decay of solutions of some nonlinear wave equations (1989-4)
  
  
• (In collaboration with R. Winther) The Korteweg-de Vries equation in a quarter plane, continuous dependence results (1989-2)
  
  

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