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.



1972 -- 1988

• (In collaboration with J.P. Albert & M. Felland) A criterion for the formation of singularities for the generalized Korteweg-de Vries equation. (1988-2)
  
  
• (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 & 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)
  
  
• (In collaboration with B,Boczar-Karakiewicz & D.L. Cohen) Interaction of Shallow-water waves and bottom topography (1987-2)
  
  
• (In collaboration with B. Boczar-Karakiewicz)Wave-Dominated Shelves : A Model of Sand-ridge formation by progressive, infragravity waves (1986-4)
  
  
• (In collaboration with D. Vassilios & O.A. Karakashian) Fully Discrete Galerkin Methods for the Korteweg-de Vries equation (1986-3)
  
  
• (In collaboration with J.-C. Saut) Singularites dispersives de solutions d'equations de type Korteweg-de Vries. (1986-1)
  
  
• (In collaboration with M.E. Schonbek) Travelling-wave solutions to the Korteweg-de Vries-Burgers equation (1985-3)
  
  
• (In collaboration with W.G. Pritchard & L.R. Scott) Numerical schemes for a model for nonlinear dispersive waves. (1985-2)
  
  
• (In collaboration with B. Boczar-Karakiewicz & G. Chapalain) On sediment transport rates and related time scales for sand bar formation in coastal zones. (1985-1)
  
  
• (In collaboration with D.K. Bose & R.E.L. Turner) Finite-amplitude steady waves in stratified fluid. (1983-4)
  
  
• (In collaboration with W.G. Pritchard & L.R. Scott) A Comparison of Solutions of Two Model Equations for Long Waves. (1983-2)
  
  
• (In collaboration with R. Winther) The Korteweg-de Vries equation, posed in a quarter-plane. (1983-1)
  
  
• (In collaboration with W.G. Pritchard & L.R. Scott) An evaluation of a model equation for water waves. (1981-3)
  
  
• On solitary waves and their role in the evolution of long waves. (1981-2)
  
  
• Solitary waves and other phenomena associated with model equations for long waves. Fluid Dynamics Transactions 10 Panstowowe Wydawnictwo Naukowe: Warszawa, pp. 77-111 (1980-7)
  
  
• Solitary waves. (1980-6)
  
  
• Model equations for waves in nonlinear dispersive systems. (1980-5)
  
  
• (In collaboration with W.G. Pritchard & L.R. Scott) A posteriori error estimates for exact and approximate solutions of time-dependent problems. (1980-4)
  
  
• (In collaboration with V. Dougalis) An Initial- and Boundary-Value problem for a model equation for propagation of long waves. (1980-3)
  
  
• (In collaboration with W.G. Pritchard & L.R. Scott) Solitary-wave interaction. (1980-1)
  
  
• (In collaboration with L.R. Scott) Solutions of the KdV equation in fractional order Sobolev spaces. (1976-3)
  
  
• (In collaboration with D.K. Bose & T.B. Benjamin) Solitary-wave solutions for some model equations for waves in nonlinear dispersive media. (1976-2)
  
  
• (In collaboration with R.W. Smith) A model for the two-way propagation of water waves in a channel. (1976-1)
  
  
• On the stability theory of solitary waves. (1975-3)
  
  
• (In collaboration with R.W. Smith) The initial-value problem for the Korteweg-de Vries equation. Philos. Trans. Royal Soc. London Series A 278, pp.555-601 (1975-1)
  
  
• (In collaboration with R.W. Smith) The initial-value problem for the Korteweg-de Vries equation. (1974-1)
  
  
• (In collaboration with G. Birkhoff & J. Kampe de Feriet) Statistically well-set Cauchy problems.(1973-2)
  
  
• (In collaboration with P.J. Bryant) A mathematical model for long waves generated by wavemakers in nonlinear dispersive systems. (1973-1)
  
  
• Fixed point theorems for Frechet spaces.(1972-2)
  
  
• (In collaboration with T.B. Benjamin & J.J. Mahony) Model equations for long waves in nonlinear dispersive systems. Philos. Trans. Royal Soc. London Series A 272, pp.47-78
  (1972-1)
  

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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