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.



Selected Recent Publications

• On the stability of the KdV multi-solitons. Diff. & Integral Eq. 20 pp.641-878 (2007-3)
  
  
• (In collaboration with V. Dougalis and D. Mitsotakis) Numerical Solutions of KdV-KdV Systems of Boussinesq equations. I. The numerical scheme and generalized solitary waves. Math & Computers in Simulation 74 pp.214-226. (2007-2)
  
  
• (In collaboration with J.-C. Saut & M. Chen) Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: Part II. Nonlinear theory. Nonlinearity 17 (2004) pp.925-952 (2004-1)
  
  
• (In collaboration with A.A. Alazman, J.P. Albert, M. Chen and J. Wu) Comparisons between the BBM equation and a Boussinesq system. Advances Diff. Eq. 11 pp. 121-166

Currently Submitted for Publication

• (In collaboration with S.-M. Sun & B.-Y Zhang) Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equation in a quarter plane.
  (2007-9)
  
  
• (In collaboration with V. Dougalis and D. Mitsotakis) Numerical Solutions of KdV-KdV Systems of Boussinesq equations. II. Generations, interactions and stability of generalized solitary waves. (2007-7)
  
  
• (In collaboration with N. Tzvetkov)
  Sharp well-posedness results for the BBM equation. (2007-4)
  
  
  

Selected Past Publications

• (In collaboration with Z. Grujic) Spatial analyticity properties of nonlinear wave equations. Math. Models & Methods in Appl. Sci 3 (2003) pp.1-15.
  
  
• (In collaboration with S.-M. Sun and B.-Y. Zhang) A Non-homogeneous Boundary-Value Problem for the Korteweg-de Vries Equation Posed on a finite domain. Commun. PDE 28 (2003) pp.1391-1736.
  
  
• (In collaboration with S.-M. Sun and B.-Y. Zhang) Forced oscillations of a damped Korteweg -de Vries equation in a quarter plane. Commun. Contemporary Math. 5 pp.369-400. (2003-3)
  
  
• (In collaboration with H. Chen) Local and global well-posedness results for generalized BBM-type equations. Evolution Equations: Proceedings in Honor of J.A. Goldstein's 60th Birthday (ed. G.R. Goldstein, R. Nagel, S. Romanelli) Marcel Dekker: New York.
  
  
• (In collaboration with B. Boczar-Karakiewicz, W. Romanczyk & E.B. Thornton ) Seasonal and interseasonal variability of sand bars at Duck, NC, USA. Observations and model predictions.
  
  
• (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 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)
  

Some Principal Collaborators

John Albert
Min Chen
Vassilios A. Dougalis
Zuran Grujic
Ohannes Karakashian
Barbara Karakiewicz
Jenny Li
Juan Restrepo
Wojtek Romanczyk
Manuel Santos
Jean-Claude Saut
Shuming Sun
Ed Thornton
Bing yu Zhang

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