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.



Stability and instability

• (In collaboration with A. Esfahani & A. Pastor) Stability of solitary-wave solutions of systems of dispersive equations. (2017-2)
  
  
• (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 D. Pilod) Stability of solitary-wave solutions to the Hironta-Satsuma equation. (2010-2)
  
  
• (In collaboration with J. Albert & N. Nguyen) On the stability of the KdV multi-solitons. (2007-3)
  
  
• (In collaboration with J. Angulo & M. Scialom) Stability of cnoidal waves. (2006-3)
  
  
• (In collaboration with Y. Liu & V. Nguyen) Stability of solitary waves in higher-order Sobolev spaces. (2004-3)
  
  
• (In collaboration with Y. Liu & M.M. Tom) The Cauchy problem and stability of solitary-wave solutions for RLW-KP--type equations. (2002-6)
  
  
• (In collaboration with J. Angulo, F. Linares & M. Scialom) Scaling, stability and singularities for nonlinear, dispersive wave equations:the critical case. (2002-3)
  
  
• (In collaboration with Y. Liu) Instability of solitary-wave solutions of the 3-dimensional Kadomtsev-Petviashvili equation. (2002-1)
  
  
• (In collaboration with A. Soyeur) On the stability of solitary-wave solutions of model equations of Long Waves (1994-3)
  
  
• (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 R. Sachs) Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation. (1988-1)
  
  
• (In collaboration with P.E. Souganidis &mp W.A. Strauss) Stability and instability of solitary waves of Korteweg-de Vries type. (1987-5)
  
  
• (In collaboration with J.P. Albert & D.B. Henry) Sufficient conditions for stability of solitary-wave solutions of model equations for long waves. (1987-3)
  
  
• On the stability of solitary waves. (1975-3)
  
  

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
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