Bernard Deconinck: Publications and Software

Software:

7. SpectrUW2.0: freeware for the computation of spectra of linear operators. See SpectrUW's project page for more information (With Firat Kiyak and J. D. Carter).

6. Abelmap, etc. Maple software for the computation of the Abel map from a Riemann surface to its Jacobian. Here are the relevant files (source, examples, instructions) for the code (with Matt Patterson ). Available in Maple 11, or later.

5. INT, SUM, etc. Maple software for the symbolic integration and summation of expressions that may or may not be exact. Here are the relevant files (source, examples, instructions) for the code (with Michael Nivala ) .

4. SpectrUW1.0: freeware for the computation of spectra of linear operators. See SpectrUW's project page for more information (With Firat Kiyak and J. D. Carter and J. Nathan Kutz ).

3. Maple software for the symbolic computation of conservation laws of (1+1)-dimensional partial differential equations. Here are instructions, examples, and the source file for the code (With Michael A. Nivala).

2. I have developed Maple software for the numerical computation of Riemann theta functions. This software is available in Maple , versions 8 or later. If you run Maple 7, you can download a version from here (with Mark van Hoeij)

1. I have developed Maple software for the computation (symbolic and numerical) of the monodromy, homology, cohomology and periodmatrix of a Riemann surface specified by a (possibly singular) plane algebraic curve. This software is available in Maple , versions 6 or later. If you still run MapleV.5, you can download a version from here.(with Mark van Hoeij)

Journal articles:

28. KdV cnoidal waves are linearly stable (with Nate Bottman) (submitted for publication) .pdf .

27. Computing the Abel map (with Matt Patterson) (submitted for publication) .pdf .

26. Symbolic integration and summation using homotopy methods (with Michael Nivala ) (submitted for publication) .pdf .

25. Nonlinear stability of plane-wave solutions of the nonlocal nonlinear Schrodinger equation (with Brandon Bale, Richard Kollar and J. Nathan Kutz ) (submitted for publication) .pdf .

24. The pole dynamics of rational solutions of the viscous Burgers equation (with Yoshifumi Kimura and Harvey Segur) Journal of Physics A 40, 5459-5467, 2007. .pdf .

23. Continuous and Discrete Homotopy Operators: A Theoretical Approach made Concrete (with Willy Hereman and L. D. Poole) (Mathematics and Computers in Simulation 74, 2007, 352-360) .pdf .

22. 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, 370-379) .pdf .

21. Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schr\"odinger equation (with R. J. Thelwell and J. D. Carter) (Journal of Physics A 39, 73-84, 2006) .pdf .

20. Instabilities of one-dimensional trivial-phase solutions of the two-dimensional cubic nonlinear Schr\"odinger equation (with J. D. Carter) (Physica D214, 42-54, 2006) .pdf .

19. Transverse instabilities of deep-water solitary waves (with D. E. Pelinovsky and J. D. Carter) (Proceedings of the Royal Society A 462, 2039-2061, 2006) .pdf .

18. Computing spectra of linear operators using Hill's method (with J. Nathan Kutz ) (J. Comp. Physics 219, 296-321, 2006) .pdf .

17. Linearly coupled Bose-Einstein Condensates: from Rabi oscillations and quasi-periodic 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 .

16. Exact nonstationary solutions of the mean-field equations of motion for two-component Bose-Einstein condensates in periodic potentials (with R. M. Bradley and J. Nathan Kutz ), (J. Phys. A 38, 2005, 1901-1916) .pdf .

15. Dynamics of periodic multi-components Bose-Einstein condensates (with J. Nathan Kutz , Matthew S. Patterson , Brandon W. Warner ) (Journal of Physics A 36, 2003, 531-547) .pdf .

14. Singular instability of exact stationary solutions of the nonlocal Gross-Pitaeskii equation (with J. Nathan Kutz ) (Physics Letters A 319, 2003, 97-103) .pdf .

13. Computing Riemann Theta Functions ( With Matthias Heil, Alexander Bobenko , Mark van Hoeij and Markus Schmies ) (Mathematics of Computation 73 (2004) 1417-1442) .pdf .

12. Dynamics and Stability of Bose-Einstein Condensates: the Nonlinear Schrodinger Equation with Periodic Potential (with Bela A. Frigyik and J. Nathan Kutz ) (J. Nonlinear Sci 12, pp 169-205, 2002) .pdf .

11. 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 177-184) .pdf .

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

9. Stability of Repulsive Bose-Einstein 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 .

8. Bose-Einstein 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 1402-1405) .pdf .

7. Computing Riemann matrices of algebraic curves (with Mark van Hoeij ) (Physica D 152-153, 2001, pp 28-46) .pdf . (Note: this is a slightly different version from the one that is published. In my opinion this version is better.)

6. Pole dynamics for elliptic solutions of the KdV equation (with Harvey Segur ) (Mathematical Physics, Analysis and Geometry 3, 2000, pp 49-74) .pdf .

5. Canonical variables for multiphase solutions of the KP equation (Studies in Applied Mathematics 104, 2000, pp 229-292) .pdf .

4. The KP equation with quasiperiodic initial data (with Harvey Segur ) (Physica D 123, 1998, pp 123-152) .pdf .

3. A constructive test for the integrability of semi-discrete systems (Physics Letters A 223, 1996, pp 45-54) .pdf .

2. 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 457-476) abstract , (Electronic version of this paper is not available)

1. 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 445-455) abstract , (Electronic version of this paper is not available)

Contributions to books:

2. 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).

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

Ph. D. Thesis: