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.



Numerical studies of dispersive PDEs

• (In collaboration with V. Dougalis & D. Mitsotakis) Numerical solutions of KdV-KdV Ssystems of Boussinesq equations. II. Evolution of radiating solitary waves. (2008-3)
  
  
• (In collaboration with V. Dougalis & D. Mitsotakis) Numerical solutions of KdV-KdV Ssystems of Boussinesq equations. I. The numerical scheme and generalized solitary waves. (2007-2)
  
  
• (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) The effect of dissipation on solutions of the generalized Korteweg-de Vries. (1996-6.1) (1996-6.2)
  
  
• (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 J.M. Restrepo) Discretization of a model for the formation of longshore sand ridges. (1995-7)
  
  
• (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 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 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 D. Vassilios & O.A. Karakashian) Fully Discrete Galerkin Methods for the Korteweg-de Vries equation. (1986-3)
  
  
• (In collaboration with W.G. Pritchard & L.R. Scott) Numerical schemes for a model for nonlinear dispersive waves. (1985-2)
  
  

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

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