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

• (In collaboration with Fred B. Weissler) Traveling Fronts of a Conservation Law with Hyper-Dissipation (2011-new)
  
  
• (In collaboration with J. Albert and N. Nguyen) 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 A. Fokas) Initial-boundary-value problems for linear and
  integrable nonlinear dispersive partial differential equations. Nonlinearity 21 pp. T195-T203 (2008-2)


• (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.
  (2008-3)
  
  
• (In collaboration with A. Fokas) Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations. (2008-1)
  

• (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. (2008-4)
  
  
• (In collaboration with N. Tzvetkov)
  Sharp well-posedness results for the BBM equation. (2007-4)
  
  
• (In collaboration with H. Chen, S.-M. Sun and B. - Y. Zhang) Approximating IVP by two-point BVP: The BBM equation. (2010-2)
  
  
  

Selected Past Publications

• (In collaboration with H. Chen, S.-M. Sun & B.-Y. Zhang) Comparison of quarter-plane and two-point boundary value problems: The BBM-equation. (2005-2)
  
  
• (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 (2006-1)
  
  
• (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 Jenny Li) Stabilizing, Monetary Injection Policies (2001-3)
  
  
• (In collaboration with W.H. McKinney & J.M. Restrepo) Stable and unstable solitary-wave solutions of the GRLW equation. (2000-5)
  
  
• (In Collaboration with H. Chen) Comparison of Model Equations for Small-Amplitude Long Waves (1999-4)
  
  
• (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 W.G. Pritchard & L.R. Scott) An Evaluation of a Model Equation for Water Waves (1981-3)
  
  
• (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 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 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)
  

Recent Collaborators

John Albert
Hongqiu Chen
Min Chen
Thierry Colin
Vassilios A. Dougalis
Hassan Fathallah-Shaykh
Thanasis Fokas
Zoran Grujic
Colette Guillope
Henryk Kalisch
Ohannes Karakashian
Barbara Karakiewicz
David Lannes
Jenny Li
Yue Liu
Dimitri Mitsotakis
Jaime Angulo Pava
Juan Restrepo
Wojtek Romanczyk
Manuel Santos
Jean-Claude Saut
Marcia Scialom
Shuming Sun
Michael Tom
Nikolay Tzvetkov
Ed Thornton
Vladimir Varlamov
Ed Vrscay
Fred Weissler
Jiahong Wu
Bing-Yu Zhang

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