Bernard Deconinck's Research

Publications (in reverse chronological order of first submission)

 On the nonintegrability of equations for long and shortwave interactions
(with J. Upsal, (submitted for publication, 2017)
.pdf.
 The timedependent Schrodinger equation with piecewise constant potentials
(with N. Sheils), (submitted for publication, 2017)
.pdf.

The stability spectrum for elliptic solutions to the sineGordon equation
(with P. McGill and Benjamin Segal) (Submitted for publication, 2017)
.pdf.

Fokas's Unified Transform Method for Linear Systems
(with Q. Guo, Eli Shlizerman and V. Vasan) (Submitted for publication, 2017)
.pdf.

The Stability Spectrum for Elliptic Solutions to the Focusing NLS
Equation
(with B. Segal) (Submitted for publication, 2016)
.pdf.

Explicit solutions for a longwave model with constant vorticity
(with B. Segal, D. Moldabayev and H. Kalisch
) (Submitted for publication, 2016)
.pdf.

The interaction of long and short waves in dispersive media (with N. Nguyen and B. Segal
) Journal of Physics A, 415501, 2016
.pdf.

The instability of Wilton ripples (with O. Trichtchenko and J. Wilkening
) (Submitted for publication, 2015)
.pdf.

The linear KdV equation with an interface (with N. Sheils and D. A. Smith
) (Submitted for publication, 2015)
.pdf.

InitialtoInterface Maps for the Heat Equation on Composite Domains (with N. Sheils
) (Submitted for publication, 2015)
.pdf.

Highfrequency instabilities of smallamplitude solutions of Hamiltonian PDEs (with O. Trichtchenko
) (Submitted for publication, 2015)
.pdf.

A method to recover waterwave profiles from pressure measurements (with V. Vasan, K. Oliveras,
D. Henderson) (Submitted for publication, 2015)
.pdf.

Computing the Riemann Constant Vector (with C. Swierczewski) (Submitted for publication, 2015)
.pdf.

Heat conduction on the ring. Interface problems with periodic boundary conditions.
(with N. E. Sheils) (Submitted for publication, 2014)
.pdf.

Interface Problems for Dispersive Equations
(with N. E. Sheils) (Submitted for publication, 2014)
.pdf.

Stability of gravity waves in the presence of surface tension
(with O. Trichtchenko) (Submitted for publication, 2013)
.pdf.

Nonsteady state heat conduction in composite walls
(with B. Pelloni and N. E. Sheils) (Submitted for publication, 2013)
.pdf.

Shortwave transverse instabilities of line solitons of the 2D hyperbolic nonlinear Schrodinger equation
(with D. E. Pelinovsky, E. A. Ruvinsakaya and O. A. Kurkina) (Theoretical and Mathematical Physics 179, pp 452461,
2014)
.pdf (English),
.pdf (Russian).

Dispersive and soliton perturbations of finitegenus solutions of the KdV equation: computational results
(with Tom Trogdon)
(Submitted for publication, 2013)
.pdf.

A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
(with Tom Trogdon)
(Submitted for publication, 2013)
.pdf.

On the spectral stability of solitary wave solutions of the vector NLS equation
(with Natalie Sheils, Nghiem V. Nguyen, Rushun Tian)
(Submitted for publication, 2013)
.pdf.

The bernoulli boundary condition for traveling water waves
(with Vishal Vasan)
(Accepted for publication, Applied Mathematics Letters, 2012)
.pdf.

Neck instability of bright solitary waves in hyperbolic Kerr media
(with SimonPierre Gorza, Tom Trogdon, Philippe Emplit, Marc Haelterman)
(Submitted for publication)
.pdf.

Numerical computation of the finitegenus solutions of the Kortewegde Vries equation via RiemannHilbert
problems
(with Tom Trogdon)
(Accepted for publication, Applied Mathematics Letters, 2012)
.pdf.

Relating the bottom pressure and the surface elevation in the water wave problem
(with Katie Oliveras and Vishal Vasan)
(Submitted for publication)
.pdf.

A RiemannHilbert problem for the finitegenus solutions of the KdV equation and its numerical solution
(with Tom Trogdon)
(Submitted for publication)
.pdf.

Global existence for a coupled system of Schrodinger equations with powertype nonlinearities
(with Nghiem V. Nguyen, Rushun Tian, and Natalie Sheils)
(J. Math. Phys. 54, 011503, 2013)
.pdf.

The inverse water wave problem of bathymetry detection
(with Vishal Vasan)
(Submitted for publication)
.pdf.

Computing Riemann Theta functions in Sage with applications
(with Chris Swierczewski)
(Submitted for publication)
.pdf.

Recovering the waterwave profile from pressure measurements
(with Katie Oliveras, Vishal Vasan, and Diane Henderson)
(Submitted for publication)
.pdf.

Numerical inverse scattering for the Kortewegde Vries and modified Kortewegde Vries equations
(with Thomas Trogdon and Sheehan Olver)
(Submitted for publication)
.pdf.

Wellposedness of boundaryvalue problems for the linear BenjaminBonaMahony equation
(with Vishal Vasan)
(Submitted for publication)
.pdf.

The instabilities of periodic traveling water waves with respect to transverse perturbations
(with Katie Oliveras)
(Submitted for publication)
.pdf.

Recovering the waterwave surface from pressure measurements
(with Diane Henderson, Katie Oliveras, and Vishal Vasan)
(Proceedings of the 10th International Conference on Mathematical and
Numerical Aspects of Waves (Refereed), WAVES 2011,
Vancouver July 2529, 2011) .pdf.

Solving linear partial differential equations
(with Thomas Trogdon and Vishal Vasan)
(SIAM Review 56, 159186)
.pdf.

Experimental demonstration of the oscillatory snake instability of the
bright soliton of the (2+1)D hyperbolic nonlinear Schrodinger
equation (with SimonPierre Gorza,
Philippe Emplit, Thomas Trogdon, and
Marc Haelterman) (Physical Review Letters 106, 094101, 2011) .pdf.
 The solution of linear constantcoefficient evolution
PDEs with periodic boundary conditions
(with Thomas Trogdon) (Accepted for publication, Applicable analysis)
.pdf.

The stability analysis of the periodic traveling wave solutions of the mKdV equation
(with Michael Nivala)
(Studies in Applied Mathematics 126, 1748, 2010)
.pdf.
 Transverse instability of bright solitons in hyperbolic dispersive media
(with SimonPierre Gorza, Philippe Emplit, Marc Haelterman, and
Thomas Trogdon) (Proceedings of the 2010 Nonlinear Photonics meeting (refereed) in Karlsruhe, Germany)
.pdf.
 The orbital stability of the cnoidal waves of the Kortewegde Vries equation
(with Todd Kapitula)
(Physics Letters A 374, 40184022, 2010)
.pdf.
 The instability of periodic surface gravity waves
(with Katie Oliveras)
(Journal of Fluid Mechanics 675, 141167, 2011)
.pdf.
 Elliptic solutions of the defocusing NLS equation are stable
(with Nate Bottman and Michael Nivala)
(Journal of Physics A 44, 285201, 2011)
.pdf.
 On the orbital (in)stability of spatially periodic stationary solutions
of generalized Kortewegde Vries equations (with Todd Kapitula)
(submitted for publication) .pdf.
 Spectral stability of stationary solutions of a Boussinesq system
describing long waves in dispersive media (with Min Chen, Chris Curtis, Crystal Lee, and Nghiem Nguyen)
(SIAM J. Applied Dynamical Systems 9, 9991018, 2010) .pdf.
 Periodic finitegenus
solutions of the KdV equation are orbitally stable (with Michael Nivala)
(Physica D 239, 11471158, 2010) .pdf .
 Data analysis and reduction
using stationary solutions of the NLS equation (with David Lovit)
(Applicable Analysis 89, 611626, 2010) .pdf
.
 On the convergence of
Hill's method (with Chris Curtis) (Mathematics of Computation 79,
169187, 2010) .pdf .
 KdV cnoidal waves are
linearly stable (with Nate Bottman) (DCDSA 25, 11631180, 2009) .pdf .
 Computing the Abel map
(with Matt Patterson) (Physica D 237, 32143232, 2008) .pdf .
 Symbolic integration and
summation using homotopy methods (with Michael Nivala)
(Mathematics and Computers in Simulation 80, 825836, 2009) .pdf .

The pole dynamics of
rational solutions of the viscous Burgers equation
(with Yoshifumi Kimura and Harvey Segur)
Journal of Physics A 40, 54595467, 2007.
.pdf .

Continuous and Discrete Homotopy Operators:
A Theoretical Approach made Concrete (with
Willy Hereman and L. D. Poole)
(Mathematics and Computers in Simulation 74, 2007, 352360)
.pdf .

SpectrUW: a laboratory for the numerical exploration of spectra of linear
operators (with Firat Kiyak,
J. D. Carter and
J. Nathan Kutz
)
(Mathematics and Computers in Simulation 74, 2007, 370379)
.pdf .

Instabilities of onedimensional stationary solutions of the
cubic nonlinear Schr\"odinger equation (with
R. J. Thelwell
and J. D. Carter)
(Journal of Physics A 39, 7384, 2006)
.pdf .

Instabilities of onedimensional trivialphase solutions of the twodimensional
cubic nonlinear Schr\"odinger equation (with
J. D. Carter)
(Physica D 214, 4254, 2006)
.pdf .

Transverse instabilities of deepwater solitary waves (with D. E. Pelinovsky and
J. D. Carter)
(Proceedings of the Royal Society A 462, 20392061, 2006)
.pdf .
 Computing spectra of linear operators
using the FloquetFourierHill method (with
J. Nathan Kutz)
(J. Comp. Physics 219, 296321, 2006)
.pdf .
 Linearly coupled BoseEinstein
Condensates: from Rabi oscillations and quasiperiodic solutions to sloshing
domain walls and spiral waves (with P. G. Kevrekidis, H. E.
Nistazakis, and D. J. Frantzeskakis) (Phys. Rev. A 70, 063605, 2004)
.pdf .
 Exact nonstationary
solutions of the meanfield equations of motion for twocomponent BoseEinstein
condensates in periodic potentials (with R. M. Bradley and J. Nathan Kutz),
(J. Phys. A 38, 2005, 19011916)
.pdf .
 Dynamics of periodic multicomponents
BoseEinstein condensates (with J. Nathan Kutz, Matthew S. Patterson,
Brandon W. Warner
)
(Journal of Physics A 36, 2003, 531547)
.pdf .
 Singular instability of exact
stationary solutions of the nonlocal GrossPitaeskii equation (with
J. Nathan Kutz)
(Physics Letters A 319, 2003, 97103)
.pdf .

Computing Riemann Theta Functions
(
With Matthias Heil, Alexander Bobenko,
Mark van Hoeij
and
Markus Schmies
)
(Mathematics of Computation 73 (2004) 14171442)
.pdf .

Dynamics and Stability of BoseEinstein Condensates:
the Nonlinear Schrodinger Equation with Periodic Potential
(with
Bela A. Frigyik
and
J. Nathan Kutz
)
(J. Nonlinear Sci 12, pp 169205, 2002)
.pdf .

Stability of exact solutions of the defocusing nonlinear
Schrodinger equation with periodic potential in two dimensions
(with
Bela A. Frigyik
and
J. Nathan Kutz
)
(Physics Letters A 283, 2001, pp 177184)
.pdf .

Stability of Attractive BoseEinstein Condensates in a Periodic Potential
(with
Jared C. Bronski,
Lincoln D. Carr,
Ricardo CarreteroGonzalez,
J. Nathan Kutz
and
K. Promislow
)
(Physical Review E 64, 2001 Ref. Nr. 056615)
.pdf .

Stability of Repulsive BoseEinstein Condensates in a Periodic Potential
(with
Jared C. Bronski,
Lincoln D. Carr,
J. Nathan Kutz
and
K. Promislow
)
(Physical Review E 63, 2001, Ref. nr. 036612)
.pdf .

BoseEinstein condensates in standing waves: the cubic nonlinear
Schrodinger equation with a periodic potential
(with
Jared C. Bronski,
Lincoln D. Carr and
J. Nathan Kutz
)
(Physical Review Letters 86, 2001, pp 14021405)
.pdf .

Computing Riemann matrices of algebraic curves
(with
Mark van Hoeij
)
(Physica D 152153, 2001, pp 2846)
.pdf .
(Note: this is a slightly different version from the one that is
published. In my opinion this version is better.)

Pole dynamics for elliptic solutions of the KdV equation
(with
Harvey Segur
)
(Mathematical Physics, Analysis and Geometry 3, 2000, pp 4974)
.pdf .

Canonical variables for multiphase solutions of the KP equation
(Studies in Applied Mathematics 104, 2000, pp 229292)
.pdf .

The KP equation with quasiperiodic initial data
(with Harvey Segur)
(Physica D 123, 1998, pp 123152)
.pdf .

A constructive test for the integrability of semidiscrete systems
(Physics Letters A 223, 1996, pp 4554)
.pdf.

Oblique nonlinear Alfven waves in strongly magnetized beam plasmas. Part 2.
soliton solutions and integrability
(with Peter Meuris and Frank Verheest)
(Journal of Plasma Physics 50, part 3, 1993, pp 457476)
abstract ,
(Electronic version of this paper is not available)

Oblique nonlinear Alfven waves in strongly magnetized beam plasmas. Part 1.
Nonlinear vector evolution equation
(with Peter Meuris and Frank Verheest)
(Journal of Plasma Physics 50, part 3, 1993, pp 445455)
abstract ,
(Electronic version of this paper is not available)

Contributions to books

 Computing with Riemann Surfaces: the algorithms of the Maple package ``algcurves'', in Lecture Notes in Mathematics, Volume 2013, Alexander Bobenko and Christian Klein, editors, Springer, 2011. .pdf (not refereed)
 Multidimensional Theta Functions, in the Digital Library of Mathematical Functions, National Institute for Standards and Technology, F. W. J. Olver, D. W. Lozier, R. F.
Boisvert, C. W. Clark, editors, Cambridge University Press, 2010. (refereed).
 Continuous and Discrete Homotopy Operators with Applications in Integrability Testing (with W. Hereman, M. Colagrosso, R. Sayers, A. Ringler, M. Nivala and M. Hickman) in Differential Equations with Symbolic computation, edited by Dongming Wang and Zhiming Zheng, Birkhauser, 2005. .pdf (refereed).

Encyclopedia of Nonlinear Science (Routhledge Publishers, 2004):
entries on KadomtsevPetviashvili equation, Periodic Spectral theory, Poisson Brackets (not refereed).