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.



Ill-posedness and singularity formation

• (In collaboration with M. Dai) Norm-inflation results for the BBM equation.. (2017-1)
  
  
• (In collaboration with G. Ponce, J.-C. Saut & C. Sparber) Dispersive blow-up for nonlinear Schrödinger equations revisited. (2014-3)
  
  
• (In collaboration with S. Vento & F.B. Weissler) Singularity formation and blowup of complex-valued soltuions of the modified KdV equation. (2013-3)
  
  
• (In collaboration with J.-C. Saut) Dispersive blow-up II. Schrödinger equations, optical and oceanic rogue waves. (2010-4)
  
  
• (In collaboration with F.B. Weissler) Pole dynamics of interacting solitons and blow-up of complex valued solutions of the KdV-equation. (2009-5)
  
  
• (In collaboration with N. Tzvetkov) Sharp well-posedness results for the BBM equation. (2009-3)
  
  
• (In collaboration with H. Kalisch) Singularity formation in the generalized Benjamin-Ono equation. (2004-4)
  
  
• (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 F.B. Weissler) Blow-up of spatially periodic complex-valued solutions of nonlinear dispersive equations. (2001-4)
  
  
• (In collaboration with F.B. Weissler) Similarity solutions of the generalized Korteweg-de Vries equation. (1999-5)
  
  
• (In collaboration with J. Angulo, F. Linares & M. Scialom) On the structure of singularities in solutions of the nonlinear Schrödinger equations for the critical case, p=4/n. (1999-2)
  
  
• (In collaboration with J.-C. Saut) Dispersive blowup of solutions of the generalized Korteweg-de Vries equations. (1993-2)
  
  
• (In collaboration with J.P. Albert & M. Felland) A criterion for the formation of singularities for the generalized Korteweg-de Vries equation. (1988-2)
  
  

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
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