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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 long-crested water waves. Discrete and Continuous Dynamical Systems 33 No 2 (2012-new)

  • (In collaboration with Fred B. Weissler) Traveling Fronts of a Conservation Law with Hyper-Dissipation (2011-new)

  • (In collaboration with H. Chen, S.-M. Sun and B. - Y. Zhang) Approximating IVP by two-point BVP: The BBM equation. (2010-2)

  • (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 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. Nonlinearity 21 pp. T195-T203 (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 N. Tzvetkov)
    Sharp well-posedness results for the BBM equation. (2007-4)

  • (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.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 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) 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 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 M. Chen & J.-C. Saut ) 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 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. Commun. Contemporary Math. 5 pp.369-400. (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) Moeling 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)

  • (In collaboration with C. Cascaval) Nonlinear dispersive waves on trees. Canadian Applied Mathematics Quarterly 16 No 1 (1998-6)

  • (In collaboration with M. Chen) A Boussinesq system for two-way propagation of nonlinear dispersive waves (1998-3)

  • (In collaboration with H. Chen) Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations (1998-1)

  • (In collaboration with Y.A. Li) Decay and analyticity of solitary waves (1997-4)

  • (In collaboration with J.P. Albert & J.-C. Saut) Model equations for waves in stratified fluids (1997-3)

  • (In collaboration with M.S. Santos) On the role of computation in economic theory (1997-1)

  • (In collaboration with V.A. Dougalis,O.A. Karakashian & W.R. McKinney) The effect of dissipation on solutions of the generalized Korteweg-de Vries (1996-6.1)   (1996-6.2)

  • (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Numerical simulation of singular solutions of the generalized Korteweg-de Vries equation. (1996-4)

  • (In collaboration with B.-Yu Zhang) The initial-value problem for the forced Korteweg-de Vries equation. (1996-3)

  • (In collaboration with Y.A. Li) Analyticity of solitary-wave solutions of model equations for long waves. (1996-2)

  • (In collaboration with H.A. Biagioni, R.J. Iorio Jr. & M. Scialom) On the Korteweg-de Vries-Kuramoto-Sivashinsky equation. (1996-1)

  • (In collaboration with K.S. Promislow & C.E. Wayne) Higher-order asymptotics of decaying solutions of some nonlinear, dispersive, dissipative wave equations. (1995-8)

  • (In collaboration with J.M. Restrepo) Discretization of a model for the formation of longshore sand ridges. (1995-7)

  • (In collaboration with M. Scialom) The effect of change in the nonlinearity and the dispersion relation of model equations for long waves. (1995-6)

  • (In collaboration with J.M. Restrepo) Three dimenstional model for the fomration of longshore sand structures on the continental shelf. (1995-5)

  • (In collaboration with L. Luo) More results on the decay of solutions to nonlinear, dispersive wave equations (1995-4)

  • (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation. (1995-3)

  • (In collaboration with L. Luo) Initial-boundary value problems for model equations for the propagation of long waves (1995-1)

  • (In collaboration with K. Promislow & G. Wayne) On the asymptotic behavior of solutions to nonlinear, dispersive, dissipative wave equations (1994-5)

  • (In collaboration with S.V. Rajopadhye & M.E. Schonbek) Models for propagation of bores I: Two dimensional theory (1994-1)

  • (In collaboration with A. Soyeur) On the stability of solitary-wave solutions of model equations of Long Waves (1993-10)

  • (In collaboration with L. Luo) Decay of solutions to nonlinear dispersive wave equations. (1993-4)

  • (In collaboration with J.-C. Saut) Dispersive blowup of solutions of the generalized Korteweg-de Vries equations (1993-2)

  • (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Numerical solution of the generalized Korteweg-de Vries-Burgers equation with adaptive Galerkin methods (1992-7)

  • (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. McKinney) Computations for blow-up and decay for periodic solutions of the generalized Korteweg-de Vries-Burgers equation (1992-6)

  • (In collaboration with F. Abergel) A mathematical theory for viscous, free-surface flows over a perturbed plane (1992-5)

  • (In collaboration with G. Ponce, J.-C. Saut & M.M. Tom) A model system for strong interaction between internal solitary waves (1992-4)

  • (In collaboration with the committee on the undergraduate program in mathematics) Undergraduate Major in the mathematical sciences. (1992-2)

  • (In collaboration with B. Boczar-Karakiewicz & B. Pelchat) Interaction of internal waves with the seabed continental shelves (1992-4)

  • (In collaboration with Y. Liu &emp M.M. Tom) The cauchy problem and stability of solitary-wave solutions for RLW-KP--type equations (1991-7)

  • (In collaboration with V.A. Dougalis, O.A. Karakashian & W.R. Mckinney) Fully-discrete methods with grid refinement for the generalized Korteweg-de Vries equation (1991-5)

  • (In collaboration with J.P. Albert) Comparisons between Model Equations for Long Waves (1991-3)

  • (In collaboration with J.P. Albert) Total positivity and the stability of internal waves in stratified fluids of finite depth (1991-1)

  • (In collaboration with T.B. Benjamin & D.K. Bose) Solitary-wave solutions of nonlinear problems (1990-1)

  • (In collaboration with L. Abdelouhab, M. Felland & J.-C. Saut)Nonlocal Models for nonlinear dispersive waves (1989-7)

  • (In collaboration with R.L. Sachs) The existence of internal solitary waves in a two-fluid system near the KdV limit (1989-6)

  • (In collaboration with C.J. Amick & M.E. Schonbek)Decay of solutions of some nonlinear wave equations (1989-4)

  • (In collaboration with R. Winther) The Korteweg-de Vries equation in a quarter plane, continuous dependence results (1989-2)

  • (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 M.E. Schonbek) Travelling-wave solutions to the Korteweg-de Vries-Burgers equation (1985-3)

  • (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.

  • 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)

  • (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
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
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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      © Jerry L. Bona. Updated: September 24, 2018