31. Integrable evolution equations for curves in the pseudoconformal S^3. (with T. Ivey)
Journal of Geometry and Physics, August 2021, 104249.
30. Integrable evolutions of twisted polygons in centro-affine R^m. (with G. Marí-Beffa)
International Mathematics Research Notices, rnaa161, July 2020. 59 pp.
29. An integrable flow for starlike curves in centroaffine space. (with T. Ivey and G. Marí-Beffa)
SIGMA 9 (2013) 022, 21 pp.
28. Squared Eigenfunctions and Linear Stability Properties of Closed Vortex Filaments. (with S.F. Keith and S. Lafortune)
Nonlinearity 24, no. 12 (2013) 3555-3583.
27. Stability of Small-amplitude Torus Knot Solutions of the Localized Induction Approximation. (with T. Ivey)
J. Phys. A: Math. Theor. 44 (2011) 335204.
26. Remarks on KdV-like Flows on Star-Shaped Curves. (with T. Ivey and G. Marí-Beffa)
Physica D, Vol. 238, no. 2 (2009), 788-797.
PDF version (arXiv:nlin.SI/0808.3593v1)
25. Finite-gap solutions of the Vortex Filament Equation: Isoperiodic Deformations. (with T. Ivey)
Journal of Nonlinear Science, Vol. 17, no. 6 (2007), 527--567.
PDF version (arXiv:nlin.SI/0612065)
24. 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)
23. Integrable dynamics of knotted vortex filaments.
Four lectures delivered at the Fourth International Conference on Geometry, integrability and quantization. Varna, Bulgaria 2003.
Geometry, integrability and quantization. I.M. Mladenov and G.L. Naber Editors. Softex, Sofia (2004), 11--50
22. 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
21. Connecting geometry, topology and spectra for finite-gap NLS potentials. (with T. Ivey)
Physica D 152-153 (2001), 9-19
PostScript version
20. Recent developments in integrable curve dynamics.
In Geometric Approaches to Differential Equations. Lecture Notes of the Australian Mathematical Society, Vol. 15 (2000), 56-99
Cambridge University Press.
PostScript version
19. Topology and sine-Gordon evolution of constant torsion curves. (with T. Ivey)
Physics Letters A 254 (1999), 170-178
PostScript version
18. 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
17. A note on a Backlund transformation for the Continuous Heisenberg Model.
Physics Letters A, 203 (1995), 333-344
Rogue Waves in Deep Water
16. Linear Instability of the Peregrine Breather: Numerical and Analytical Investigations. (with C.M. Schober)
Applied Numerical Mathematics, 141 (2020), pp. 36-43
15. Characterizing JONSWAP Rogue Waves and their Statistics via Inverse Spectral Data. (with C.M. Schober)
Wave Motion, 71 (2017), pp. 5-17
14. Numerical investigation of stability of breather-type solutions of the nonlinear Schroedinger equation. (with C.M. Schober)
Nat. Hazards Earth Syst. Sci., 14, (2014)
13. Observable and reproducible rogue waves. (with C.M. Schober)
J. Optics, 15, no. 10, 105201 (2013)
12. Dynamical Criteria for Rogue Waves in NLS Models. (with C.M. Schober)
Nonlinearity, 25, (2012), 19 pp.
11. Rogue Waves in Higher-Order Nonlinear Schroedinger Models. (with C. Schober)
in Extreme Ocean Waves, E. Pelinovsky and C. Kharif Editors. Springer (2008), 31--52
PDF version
10. Homoclinic chaos increases the likelihood of rogue wave formation. (with C. Schober)
Physics Letters A , 298 (5-6) (2002), 335-349
PDF version
9. 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
8. 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
7. 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
Mathematical Physics
6. Schwarz Reflection Geometry II: Local and Global Behavior of the Exponential Map. (with J. Langer)
Experimental Mathematics, Vol 16, no. 3 (2007), 321--346
PDF version
5. Schwarz Reflection Geometry I: Continuous Iteration of Reflection. (with J. Langer)
Mathematische Zeitschrift, Vol. 244, No. 4 (2003), 775-804
PDF version
Encyclopedia Articles
4. The Mel'nikov Method,
Encyclopedia of Nonlinear Science
Ed. Alwyn Scott, New York and London: Routledge, 2004.
3. Elliptic Functions,
Encyclopedia of Nonlinear Science
Ed. Alwyn Scott, New York and London: Routledge, 2004.
Theses
2. Integrable Curve Dynamics.
Ph.D. Dissertation. University of Arizona, 1994.
Advisor: Nicholas Ercolani.
1. Influenza di un Segnale Esterno sulla Dinamica Cooperativa di un Gas Atomico: Risultati Analitici.
Tesi di Laurea. Universitá degli Studi di Milano, 1989.
Advisor: Vincenzo Benza.