Geometrical aspects of soliton equations

A note on a Backlund transformation for the Continuous Heisenberg Model.
Physics Letters A, 203 (1995), 333-344.

Backlund transformations and knots of constant torsion. (with T. Ivey)
Journal of Knot Theory and its Ramifications Vol. 7 No. 6 (1998), 719-746
PostScript version

Topology and sine-Gordon evolution of constant torsion curves. (with T. Ivey)
Physics Letters A 254 (1999), 170-178
PostScript version

Recent developments in integrable curve dynamics.
In Geometric Approaches to Differential Equations. Lecture Notes of the Australian Mathematical Society, Vol. 15, p. 56-99, 2000.
Cambridge University Press.
PostScript version

Knot types, Floquet spectra, and finite-gap solutions of the Vortex Filament Equation. (with T. Ivey)
Journal of Mathematics and Computers in Simulation. Vol. 55, No. 4-6 (2001), 341-350
PDF version

Connecting geometry, topology and spectra for finite-gap NLS potentials. (with T. Ivey)
Physica D 152-153 (2001), 9-19.
PostScript version

Integrable dynamics of knotted vortex filaments. Four lectures delivered at the Fourth International Conference on Geometry,
integrability and quantization, Varna, Bulgaria.
Geometry, integrability and quantization. I.M. Mladenov and G.L. Naber Editors. Softex, Sofia (2004), 11--50.
PDF version

Finite-gap solutions of the Vortex Filament Equation: Genus one solutions and symmetric solutions. (with T. Ivey)
Journal of Nonlinear Science. Vol 15, no. 5 (2005), 321--361.
PDF version (arXiv:nlin.SI/0411065)

Finite-gap solutions of the Vortex Filament Equation: Isoperiodic Deformations. (with T. Ivey)
To appear in the Journal of Nonlinear Science (2007).
PDF version (arXiv:nlin.SI/0612065)

Dynamical Systems Methods for Perturbations of Soliton Equations.

Mel'nikov analysis of numerically induced chaos in the Nonlinear Schroedinger Equation. (with N.M. Ercolani, D.W. McLaughlin, C.M. Schober)
Physica D 89 (1996), 227-260

Mel'nikov analysis of a Hamiltonian Perturbation of the Nonlinear Schroedinger Equation. (with C. Schober)
NATO Science Series C, Math. and Phys. Sci., Vol 533. Kluwer Academic Press (1999), 558-562
PostScript version

Chaotic Dynamics for a Symmetry-Breaking perturbation of the NLS equation. (with C. Schober)
Journal of Mathematics and Computers in Silmulation. Vol. 55, No. 4-6 (2001), 351-364
PostScript version

Homoclinic chaos increases the likelihood of rogue wave formation. (with C. Schober)
Physics Letters A , 298 (5-6) (2002), pp 335-349
PDF version

Mathematical Physics

Schwarz Reflection Geometry I: Continuous Iteration of Reflection. (with J. Langer)
Mathematische Zeitschrift, Vol. 244, No. 4 (2003) , pp. 775-804
PDF version
 
Schwarz Reflection Geometry II: Local and Global Behavior of the Exponential Map. (with J. Langer)
To appear in Experimental Mathematics (2007)

Encyclopedia Articles

Entries: The Mel'nikov Method, Elliptic Functions.
Encyclopedia of Nonlinear Science
Ed. Alwyn Scott, New York and London: Routledge, 2004