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A simple formula for the conserved charges of soliton theories (2007)
Journal Article
Ferreira, L. A., & Zakrzewski, W. (2007). A simple formula for the conserved charges of soliton theories. Journal of High Energy Physics, 2007(09), https://doi.org/10.1088/1126-6708/2007/09/015

We present a simple formula for all the conserved charges of soliton theories, evaluated on the solutions belonging to the orbit of the vacuum under the group of dressing transformations. For pedagogical reasons we perform the explicit calculations f... Read More about A simple formula for the conserved charges of soliton theories.

Adiabatic self-trapped states in carbon nanotubes (2007)
Journal Article
Brizhik, L., Eremko, A., Piette, B., & Zakrzewski, W. (2007). Adiabatic self-trapped states in carbon nanotubes. Journal of Physics: Condensed Matter, 19(30), https://doi.org/10.1088/0953-8984/19/30/306205

We study the polaron (soliton) states of a quasiparticle (electron, hole, exciton) in a quasi-one-dimensional (quasi-1D) model which describes a carbon-type zigzag nanotube structure. In the Hamiltonian of the system we include the electron–phonon in... Read More about Adiabatic self-trapped states in carbon nanotubes.

Scattering of Sine-Gordon kinks on potential wells (2007)
Journal Article
Piette, B., & Zakrzewski, W. (2007). Scattering of Sine-Gordon kinks on potential wells. Journal of Physics A: Mathematical and Theoretical, 40(22), 5995-6010. https://doi.org/10.1088/1751-8113/40/22/016

We study the scattering properties of sine-Gordon kinks on obstructions in the form of finite size potential 'wells'. We model this by making the coefficient of the cos(phiv) − 1 term in the Lagrangian position dependent. We show that when the kinks... Read More about Scattering of Sine-Gordon kinks on potential wells.

Self-trapped electron states in carbon nanotubes (2007)
Journal Article
Bratek, L., Brizhik, L., Eremko, A., Piette, B., Watson, M., & Zakrzewski, W. (2007). Self-trapped electron states in carbon nanotubes. Physica D: Nonlinear Phenomena, 228(2), 130-139. https://doi.org/10.1016/j.physd.2007.02.013

We study numerically self-trapped (polaron) states of quasiparticles (electrons or holes) in a deformable nanotube formed by a hexagonal lattice, wrapped into a cylinder (carbon- and boron nitride-type nanotube structures). We present a Hamiltonian f... Read More about Self-trapped electron states in carbon nanotubes.

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.

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 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

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.

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.