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.



1999 -- 2008

• (In collaboration with C. Cascaval) Nonlinear dispersive waves on trees. (2008-6)
  
  
• (In collaboration with H. M. Fathallah-Shaykh) Approximation by cubic splines generates highly specific discovery by microarrays. (2008-5)
  
  
• (In collaboration with S.M. Sun & B.-Y. Zhang) Non-homogeneous boundary value problems for the Korteweg-de Vries-Burgers equation in a quarter plane. (2008-4)
  
  
• (In collaboration with V. Dougalis & D. Mitsotakis) Numerical Solutions of KdV-KdV Systems of Boussinesq equations. II. Evolution of radiating solitary waves. (2008-3)
  
  
• (In collaboration with D. Lannes & J.-C. Saut) Asymptotic models for internal waves. (2008-2)
  
  
• (In collaboration with A. Fokas) Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations. (2008-1)
  
  
• (In collaboration with J. Albert & N. Nguyen) On the stability of the KdV multi-solitons. (2007-3)
  
  
• (In collaboration with V. Dougalis & D. Mitsotakis) Numerical solutions of KdV-KdV Ssystems of Boussinesq equations. I. The numerical scheme and generalized solitary waves. (2007-2)
  
  
• (In collaboration with H. Chen, S.-M Sun & B.-Y. Zhang) Comparison of quarter-plane and two-point boundary value problems: The KdV-equation. (2007-1)
  
  
• (In collaboration with F. Vaince & H. M. Fathallah-Shaykh) Microarray data analysis: Current practices and future directions. (2006-5)
  
  
• (In collaboration with Z. Grujic & H. Kalisch) Global solutions of the derivative Schrödinger equation in a class of functions analytic in a strip. (2006-4)
  
  
• (In collaboration with J. Angulo & M. Scialom) Stability of cnoidal waves.(2006-3)
  
  
• (In collaboration with S.M. Sun & B.Y. Zhang) Boundary smoothing properties of the Korteweg-de Vries equation in a quarter plane and applications. (2006-2)
  
  
• (In collaboration with A.A. Alazman, J.P. Albert, M. Chen & J. Wu) Comparisons between the BBM equation and a Boussinesq system. (2006-1)
  
  
• (In collaboration with T. Colin & D. Lannes ) Long wave approximations for water waves. (2005-6)
  
  
• (In collaboration with E. Vrscay) Continuous evolution of functions and measures toward fixed points of contraction mappings. (2005-5)
  
  
• (In collaboration with Z. Grujic & H. Kalisch) Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation. (2005-4)
  
  
• (In collaboration with W. Romanczyk & B. Boczar-Karakiewicz) Extended equilibrium beach profiles. (2005-3)
  
  
• (In collaboration with H. Chen, S.-M. Sun & S.-M. Sun) Comparison of quarter-plane and two-point boundary values problems: the BBM-equation. (2005-2)
  
  
• (In collaboration with V.V. Varlamov) Wave generation by a moving boundary. (2005-1)
  
  
• (In collaboration with H. Kalisch) Singularity formation in the generalized Benjamin-Ono equation. (2004-4)
  
  
• (In collaboration with Y. Liu & V. Nguyen) Stability of solitary waves in higher-order Sobolev spaces. (2004-3)
  
  
• (In collaboration with S.-M. Sun and B.-Y. Zhang) Conditional and unconditional well-posedness for nonlinear evolution equations. (2004-2)
  
  
• (In collaboration with M. Chen & J.-C. Saut ) Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: Part II. Nonlinear theory. (2004-1)
  
  
• (In collaboration with H. Chen) Local and global well-posedness results for generalized BBM-type equations. (2003-4)
  
  
• (In collaboration with S.-M. Sun and B.-Y. Zhang) Forced oscillations of a damped Korteweg -de Vries equation in a quarter plane. (2003-3)
  
  
• (In collaboration with Z. Grujic) Spatial analyticity properties of nonlinear waves. (2003-2)
  
  
• (In collaboration with S.-M. Sun and B.-Y. Zhang) A nonhomogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain. (2003-1)
  
  
• (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. Wu) The zero-viscosity limit of the 2D Navier-Stokes equations. (2002-5)
  
  
• (In collaboration with M.Chen & J.-C. Saut) Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory. (2002-4)
  
  
• (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 H. Chen) Solitary waves in nonlinear dispersive systems. (2002-2)
  
  
• (In collaboration with Y. Liu) Instability of solitary-wave solutions of the 3-dimensional Kadomtsev-Petviashvili equation. (2002-1)
  
  
• (In collaboration with S.-M. Sun & B.-Y. Zhang) A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane. (2001-5)
  
  
• (In collaboration with F.B. Weissler) Blow-up of spatially periodic complex-valued solutions of nonlinear dispersive equations. (2001-4)
  
  
• (In collaboration with Jenny Li) Stabilizing, Monetary Injection Policies (2001-3)
  
  
• (In collaboration with L. Luo) Asymptotic decomposition of nonlinear, dispersive wave equations with dissipation (2001-2)
  
  
• (In collaboration with W.H. McKinney & J.M. Restrepo) Stable and unstable solitary-wave solutions of the GRLW equation. (2000-5)
  
  
• Nonlinear wave phenomena. (2000-4)
  
  
• (In collaboration with J. Wu) Zero-dissipation limit for nonlinear waves (2000-2)
  
  
• (In collaboration with H. Kalisch) Models for internal waves in deep water (2000-1)
  
  
• (In collaboration with B.Boczar-Karakiewicz, W. Romanczyk & E.B. Thornton) Modeling the dynamics of a bar system at Duck, NC, USA. (1999-7)
  
  
• (In collaboration with J.P. Albert & J.M. Restrepo) Solitary-wave solutions of the Benjamin equation. (1999-6)
  
  
• (In collaboration with F.B. Weissler) Similarity solutions of the generalized Korteweg-de Vries equation (1999-5)
  
  
• (In Collaboration with H. Chen) Comparison of Model Equations for Small-Amplitude Long Waves (1999-4)
  
  
• (In collaboration with F. Demengel & K. Promislow) Fourier splitting and dissipation of nonlinear dispersive waves (1999-3)
  
  
• (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 L. Luo) A generalized Korteweg-de Vries equation in a quarter plane (1999-1)
  
  

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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