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Dynamical properties of a Soliton in a Potential Well (2007)
Journal Article
Piette, B., & Zakrzewski, W. (2007). Dynamical properties of a Soliton in a Potential Well. Journal of Physics A: Mathematical and Theoretical, 40(2), 329-346. https://doi.org/10.1088/1751-8113/40/2/011

We analyse the scattering of a two-dimensional soliton on a potential well. We show that this soliton can pass through the well, bounce back or become trapped and we study the dependence of the critical velocity on the width and the depth of the well... Read More about Dynamical properties of a Soliton in a Potential Well.

Mass Terms in the Skyrme Model (2006)
Presentation / Conference Contribution
Kopeliovich, V., Piette, B., & Zakrzewski, W. (2006). Mass Terms in the Skyrme Model.

We consider various forms of the mass term for the Skyrme model and their implications on the properties of baryonic states. We show that modifications of the mass term, without changing the asymptotic behaviour of the profile function at large r, ca... Read More about Mass Terms in the Skyrme Model.

Electron self-trapping on a nano-circle. (2006)
Journal Article
Brizhik, L., Eremko, A., Piette, B., & Zakrzewski, W. (2006). Electron self-trapping on a nano-circle. Physica D: Nonlinear Phenomena, 218(1), 36-55. https://doi.org/10.1016/j.physd.2006.04.010

We study the self-trapping of quasiparticles (electrons, holes or excitons) in a molecular chain with the structure of a ring, taking into account the electron–phonon interaction and the radial and tangential deformations of the chain. A discrete sys... Read More about Electron self-trapping on a nano-circle..

Charge and energy transfer by solitons in low-dimensional nanosystems with helical structure (2006)
Journal Article
Brizhik, L., Eremko, A., Piette, B., & Zakrzewski, W. (2006). Charge and energy transfer by solitons in low-dimensional nanosystems with helical structure. Chemical Physics, 324(1), 259-266. https://doi.org/10.1016/j.chemphys.2006.01.033

We study the nonlinear mechanism of the energy and charge transfer in low-dimensional nanosystems with helical structure. We show that the helical symmetry is important for the formation, stability and dynamical properties of the soliton-like self-tr... Read More about Charge and energy transfer by solitons in low-dimensional nanosystems with helical structure.

Scattering of Topological Solitons on Holes and Barriers (2005)
Journal Article
Piette, B., Zakrzewski, W., & Brand, J. (2005). Scattering of Topological Solitons on Holes and Barriers. Journal of Physics A: Mathematical and General, 38(38), 10403-10412. https://doi.org/10.1088/0305-4470/38/48/011

We study the scattering properties of topological solitons on obstructions in the form of holes and barriers. We use the 'new baby Skyrme' model in (2 + 1) dimensions and we model the obstructions by making the coefficient of the baby Skyrme model po... Read More about Scattering of Topological Solitons on Holes and Barriers.

Scattering of periodic solitons (2005)
Journal Article
Cova, R., & Zakrzewski, W. (2005). Scattering of periodic solitons. Revista mexicana de física, 50, 527-535

Solitons and Deformed Lattices (2005)
Journal Article
Hartmann, B., & Zakrzewski, W. (2005). Solitons and Deformed Lattices. Journal of Nonlinear Mathematical Physics, 12, 88-104

Laplacians on Lattices (2005)
Journal Article
Zakrzewski, W. (2005). Laplacians on Lattices. Journal of Nonlinear Mathematical Physics, 12, 530-538

A simple model of the charge transfer in DNA-like substances (2005)
Journal Article
Walet, N., & Zakrzewski, W. (2005). A simple model of the charge transfer in DNA-like substances. Nonlinearity, 18(6), 2615-2636. https://doi.org/10.1088/0951-7715/18/6/011

We present a very simple model for the study of charge transport in a molecule patterned on B-DNA. In this model we use a discrete nonlinear Schrödinger equation to describe electrons propagating along the sugar-phosphate backbone of the DNA molecule... Read More about A simple model of the charge transfer in DNA-like substances.

Planar Skyrmions: vibrational modes and dynamics (2005)
Journal Article
Piette, B., & Ward, R. (2005). Planar Skyrmions: vibrational modes and dynamics. Physica D: Nonlinear Phenomena, 201(1-2), 45-55. https://doi.org/10.1016/j.physd.2004.12.001

We study Skyrmion dynamics in a (2+1)-dimensional Skyrme model. The system contains a dimensionless parameter α, with α=0 corresponding to the O(3) sigma-model. If two Skyrmions collide head-on, then they can either coalesce or scatter—this depends o... Read More about Planar Skyrmions: vibrational modes and dynamics.