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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.
Publications
 (In collaboration with T. Colin and C. Guillope) Propagation of longcrested water waves. Discrete and Continuous Dynamical Systems 33 No 2 (2012new)
 (In collaboration with Fred B. Weissler) Traveling Fronts of a Conservation Law with HyperDissipation (2011new)
 (In collaboration with H. Chen, S.M. Sun and B.  Y. Zhang) Approximating IVP by twopoint BVP: The BBM equation. (20102)
 (In collaboration with V. Dougalis and D. Mitsotakis) Numerical Solutions of KdVKdV Systems of Boussinesq equations. II. Generations, interactions and stability of generalized solitary waves. (20084)
 (In collaboration with S.M. Sun & B.Y Zhang) Nonhomogeneous boundary value problems for the Kortewegde Vries and the Kortewegde VriesBurgers equation in a quarter plane.
(20083)
 (In collaboration with A. Fokas) Initialboundaryvalue problems for linear and
integrable nonlinear dispersive partial differential
equations. Nonlinearity 21 pp. T195T203 (20082)
 (In collaboration with A. Fokas) Initialboundaryvalue problems for linear and integrable nonlinear dispersive partial differential equations. (20081)
 (In collaboration with N. Tzvetkov)
Sharp wellposedness results for the BBM equation.
(20074)
 (In collaboration with J. Albert and N. Nguyen) On the stability of the KdV multisolitons. Diff. & Integral Eq. 20 pp.641878 (20073)
 (In collaboration with V. Dougalis and D. Mitsotakis) Numerical Solutions of KdVKdV Systems of Boussinesq equations. I. The numerical scheme and generalized solitary waves. Math & Computers in Simulation 74 pp.214226. (20072)
 (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. 121166 (20061)
 (In collaboration with T. Colin & D. Lannes ) Long wave approximations for water waves. (20056)
 (In collaboration with E. Vrscay)Continuous evolution of functions and measures toward fixed points of contraction mappings. (20055)
 (In collaboration with Z. Grujic & H. Kalisch) Algebraic lower bounds for the uniform radius of spatial analyticity for the generalized KdV equation. (20054)
 (In collaboration with W. Romanczyk & B. BoczarKarakiewicz) Extended equilibrium beach profiles. (20053)
 (In collaboration with H. Chen & S.M. Sun) Comparison of quarterplane and twopoint boundary values problems: the BBMequation. (20052)
 (In collaboration with V.V. Varlamov) Wave generation by a moving boundary. (20051)
 (In collaboration with H. Kalisch) Singularity formation in the generalized BenjaminOno equation. (20044)
 (In collaboration with Y. Liu & V. Nguyen) Stability of solitary waves in higherorder Sobolev spaces. (20043)
 (In collaboration with S.M. Sun and B.Y. Zhang) Conditional and unconditional wellposedness for nonlinear evolution equations. (20042)
 (In collaboration with H. Chen, S.M. Sun & B.Y. Zhang) Comparison of quarterplane and twopoint boundary value problems: The BBMequation. (20052)
 (In collaboration with M. Chen & J.C. Saut ) Boussinesq equations
and other systems for smallamplitude long waves in nonlinear dispersive
media: Part II. Nonlinear theory. Nonlinearity 17 (2004) pp.925952 (20041)
 (In collaboration with H. Chen) Local and global wellposedness results for generalized BBMtype equations. (20034)
 (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.369400. (20033)
 (In collaboration with Z. Grujic) Spatial analyticity properties of nonlinear waves. (20032)
 (In collaboration with S.M. Sun and B.Y. Zhang) A nonhomogeneous boundaryvalue problem for the Kortewegde Vries equation posed on a finite domain. (20031)
 (In collaboration with Y. Liu & M.M. Tom) The Cauchy problem and stability of solitarywave solutions for RLWKPtype equations. (20026)
 (In collaboration with J. Wu) The zeroviscosity limit of the 2D NavierStokes equations. (20025)
 (In collaboration with M.Chen & J.C. Saut) Boussinesq Equations and Other Systems for SmallAmplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory. (20024)
 (In collaboration with J. Angulo, F. Linares & M. Scialom) Scaling, stability and singularities for nonlinear, dispersive wave equations:the critical case. (20023)
 (In collaboration with H. Chen) Solitary waves in nonlinear dispersive systems. (20022)
 (In collaboration with Y. Liu) Instability of solitarywave solutions of the 3dimensional KadomtsevPetviashvili equation. (20021)
 (In collaboration with S.M. Sun & B.Y. Zhang) A nonhomogeneous boundaryvalue problem for the Kortewegde Vries equation in a quarter plane. (20015)
 (In collaboration with F.B. Weissler) Blowup of spatially periodic complexvalued solutions of nonlinear dispersive equations. (20014)
 (In collaboration with Jenny Li) Stabilizing, Monetary Injection Policies (20013)
 (In collaboration with L. Luo) Asymptotic decomposition of nonlinear, dispersive wave equations with dissipation (20012)
 (In collaboration with W.H. McKinney & J.M. Restrepo) Stable and unstable solitarywave solutions of the GRLW equation. (20005)
 Nonlinear wave phenomena. (20004)
 (In collaboration with J. Wu) Zerodissipation limit for nonlinear waves (20002)
 (In collaboration with H. Kalisch) Models for internal waves in deep water (20001)
 (In collaboration with B.BoczarKarakiewicz, W. Romanczyk & E.B. Thornton) Moeling the dynamics of a bar system at Duck, NC, USA. (19997)
 (In collaboration with J.P. Albert & J.M. Restrepo) Solitarywave solutions of the Benjamin equation. (19996)
 (In collaboration with F.B. Weissler) Similarity solutions of the generalized Kortewegde Vries equation (19995)
 (In Collaboration with H. Chen) Comparison of Model Equations for SmallAmplitude Long Waves (19994)
 (In collaboration with F. Demengel & K. Promislow) Fourier splitting and dissipation of nonlinear dispersive waves (19993)
 (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. (19992)
 (In Collaboration with L. Luo) A generalized Kortewegde Vries equation in a quarter plane (19991)
 (In collaboration with C. Cascaval) Nonlinear dispersive waves on trees. Canadian Applied Mathematics Quarterly 16 No 1 (19986)
 (In collaboration with M. Chen) A Boussinesq system for twoway propagation of nonlinear dispersive waves (19983)
 (In collaboration with H. Chen) Existence and asymptotic properties of solitarywave solutions of Benjamintype equations (19981)
 (In collaboration with Y.A. Li) Decay and analyticity of solitary waves (19974)
 (In collaboration with V.A. Dougalis,O.A. Karakashian & W.R. McKinney) The effect of dissipation on solutions of the generalized Kortewegde Vries (19966.1) (19966.2)
 (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Numerical simulation of singular solutions of the generalized Kortewegde Vries equation. (19964)
 (In collaboration with B.Yu Zhang) The initialvalue problem for the forced Kortewegde Vries equation. (19963)
 (In collaboration with Y.A. Li) Analyticity of solitarywave solutions of model equations for long waves. (19962)
 (In collaboration with H.A. Biagioni, R.J. Iorio Jr. & M. Scialom) On the Kortewegde VriesKuramotoSivashinsky equation. (19961)
 (In collaboration with K.S. Promislow & C.E. Wayne) Higherorder asymptotics of decaying solutions of some nonlinear, dispersive, dissipative wave equations. (19958)
 (In collaboration with J.M. Restrepo) Discretization of a model for the formation of longshore sand ridges. (19957)
 (In collaboration with J.M. Restrepo) Three dimenstional model for the fomration of longshore sand structures on the continental shelf. (19955)
 (In collaboration with L. Luo) More results on the decay of solutions to nonlinear, dispersive wave equations. (19954)
 (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Conservative, highorder numerical schemes for the generalized Kortewegde Vries equation. (19953)
 (In collaboration with L. Luo) Initialboundary value problems for model equations for the propagation of long waves. (19951)
 (In collaboration with K. Promislow & G. Wayne) On the asymptotic behavior of solutions to nonlinear, dispersive, dissipative wave equations. (19945)
 (In collaboration with L. Luo) Decay of solutions to nonlinear dispersive wave equations. (19934)
 (In collaboration with J.C. Saut) Dispersive blowup of solutions of the generalized Kortewegde Vries equations. (19932)
 (In collaboration with S.V. Rajopadhye & M.E. Schonbek) Models for propagation of bores I: Two dimensional theory. (19941)
 (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Numerical solution of the generalized Kortewegde VriesBurgers equation with adaptive Galerkin methods (19927)
 (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Computations for blowup and decay for periodic solutions of the generalized Kortewegde VriesBurgers equation (19926)
 (In collaboration with F. Abergel) A mathematical theory for viscous, freesurface flows over a perturbed plane (19925)
 (In collaboration with G. Ponce, J.C. Saut & M.M. Tom) A model system for strong interaction between internal solitary waves (19924)
 (In collaboration with B. BoczarKarakiewicz & B. Pelchat) Interaction of internal waves with the seabed continental shelves (19924)
 (In collaboration with J.P. Albert) Comparisons between Model Equations for Long Waves (19913)
 (In collaboration with J.P. Albert) Total positivity and the stability of internal waves in stratified fluids of finite depth (19911)
 (In collaboration with T.B. Benjamin & D.K. Bose) Solitarywave solutions of nonlinear problems (19901)
 (In collaboration with L. Abdelouhab, M. Felland & J.C. Saut)Nonlocal Models for nonlinear dispersive waves (19897)
 (In collaboration with R.L. Sachs) The existence of internal solitary waves in a twofluid system near the KdV limit (19896)
 (In collaboration with C.J. Amick & M.E. Schonbek)Decay of solutions of some nonlinear wave equations (19894)
 (In collaboration with R. Winther) The Kortewegde Vries equation in a quarter plane, continuous dependence results (19892)
 (In collaboration with P.E. Souganidis & W.A. Strauss) Stability and instability of solitary waves of Kortewegde Vries type (19875)
 (In collaboration with J.P. Albert & D.B. Henry) Sufficient conditions for stability of solitarywave solutions of model equations for long waves (19873)
 (In collaboration with B,BoczarKarakiewicz & D.L. Cohen) Interaction of Shallowwater waves and bottom topography (19872)
 (In collaboration with B,BoczarKarakiewicz)WaveDominated Shelves : A Model of Sandridge formation by progressive, infragravity waves (19864)
 (In collaboration with D. Vassilios & O.A. Karakashian) Fully Discrete Galerkin Methods for the Kortewegde Vries equation (19863)
 (In collaboration with M.E. Schonbek) Travellingwave solutions to the Kortewegde VriesBurgers equation (19853)
 (In collaboration with W.G. Pritchard & L.R. Scott) A Comparison of Solutions of Two Model Equations for Long Waves (19832)
 (In collaboration with W.G. Pritchard & L.R. Scott) An Evaluation of a Model Equation for Water Waves (19813)
 (In collaboration with H. Chen) Local and global wellposedness results
for generalized BBMtype 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. BoczarKarakiewicz, W. Romanczyk & E.B.
Thornton ) Seasonal and interseasonal variability of sand bars at Duck,
NC, USA. Observations and model predictions.
 Solitary waves and other phenomena associated with model equations for long waves. Fluid Dynamics Transactions 10 Panstowowe Wydawnictwo Naukowe: Warszawa, pp. 77111 (19807)
 (In collaboration with W.G. Pritchard & L.R. Scott) Solitarywave interaction. (19801)
 (In collaboration with L.R. Scott) Solutions of the KdV equation in fractional order Sobolev spaces. (19763)
 (In collaboration with R.W. Smith) The initialvalue problem for the Kortewegde Vries equation. Philos. Trans. Royal Soc. London Series A 278, pp.555601 (19751)
 (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.4778
(19721)


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