arXiv subjects

Wojtek Zakrzewski

Publications and source records attributed to Wojtek Zakrzewski.

10 recordsLinked to original sources

arXiv2017

Aspects of the modified regularized long-wave equation

We study various properties of the soliton solutions of the modified regularized long-wave equation. This model possesses exact one- and two-soliton solutions but no other solutions are known. We show that numerical three-soliton configurations, for which the initial conditions were taken in the form of a linear superposition of three single-soliton solutions, evolve in time as three-soliton solutions of the model and in their scatterings each individual soliton experiences a total phase-shift that is the sum of pairwise phase-shifts. We also investigate the soliton resolution conjecture for this equation, and find that individual soliton-like lumps initially evolve very much like lumps for integrable models but eventually (at least) some blow-up, suggesting basic instability of the model.

nlin.PS↗

arXiv2015

Collective coordinate approximation to the scattering of solitons in modified NLS and sine-Gordon models

We investigate the validity of collective coordinate approaximations to the scattering of solitons in several classes of models in (1+1) dimensional field theory models. We look at models which are deformations of the sine-Gordon (SG) or the nonlinear Schrödinger (NLS) model as they posses solitons which are topological (SG) or non-topological (NLS). Our deformations preserve their topology (SG), but changes their integrability properties, either completely or partially (models become `quasi-integrable'). As our collective coordinate approximation does not allow for the radiation of energy out the system we look also, in some detail, at how good this approximation is for models which are `quasi-integrable'. Our results are based on the studies of the interactions and scatterings in two soliton systems. Our results show that a well chosen approximation, based on geodesic motion etc, works amazingly well in all cases where it is expected to work. This is true for the trajectories of the solitons and even for their quasi-conserved (or not) charges. The only time the approximation is not very reliable (and even then the qualitative features are reasonable, but some details are not reproduced well) involves the processes when the solitons, during their scattering, can come very close together (within one width of each other).

hep-th↗

arXiv2005

The transition of 2-dimensional solitons to 1-dimensional ones on hexagonal lattices

We study solitons arising in a system describing the interaction of a two-dimensional discrete hexagonal lattice with an additional electron field (or, in general, an exciton field). We assume that this interaction is electron-phonon-like. In our previous paper [4], we have studied the existence of two-dimensional solitons and have found that these solitons exist only if the electron-phonon coupling constant is sufficiently large. In this paper, we report the results of our investigation for small values of this constant, close to its critical value for the existence of solitons. We find that as the coupling decreases the soliton gets very broad and then becomes effectively one-dimensional.

cond-mat.str-el↗

arXiv2004

Laplacians on lattices

We consider some lattices and look at discrete Laplacians on these lattices. In particular we look at solutions of the equation $\triangle(1)ϕ= \triangle(2)Z$ where $\triangle(1)$ and $\triangle(2)$ are two such laplacians on the same lattice. We discuss solutions of this equation in some special cases.

hep-th↗

arXiv2004

Axially symmetric SU(3) Gravitating Skyrmions

Axially symmetric gravitating multi-skyrmion configurations are obtained using the harmonic map ansatz introduced in [1]. In particular, the effect of gravity on the energy and baryon densities of the SU(3) non-gravitating multi-skyrmion configurations is studied in detail.

gr-qc↗

arXiv2004

An Improved Harmonic Map Ansatz

The rational map ansatz of Houghton et al \cite{HMS} is generalised by allowing the profile function, usually a function of $r$, to depend also on $z$ and $\bar{z}$. It is shown that, within this ansatz, the energies of the lowest $B=2,3,4$ field configurations of the SU(2) Skyrme model are closer to the corresponding values of the true solutions of the model than those obtained within the original rational map ansatz. In particular, we present plots of the profile functions which do exhibit their dependence on $ z$ and $\bar{z}$. The obvious generalisation of the ansatz to higher SU(N) models involving the introduction of more projectors is briefly mentioned.

hep-th↗

arXiv1998

Lagrangian Formulation of the General Modified Chiral Model

We present a Lagrangian formulation for the general modified chiral model. We use it to discuss the Hamiltonian formalism for this model and to derive the commutation relations for the chiral field. We look at some explicit examples and show that the Hamiltonian, containing a contribution involving a Wess-Zumino term, is conserved, as required.

hep-th↗

arXiv1998

A Note on Ward's Chiral Model

A one parameter generalization of Ward's chiral model in 2+1 dimensions is given. Like the original model the present one is integrable and possesses a positive-definite and conserved energy and $y$-momentum. The details of the scattering depend on the value of the parameter of the generalisation.

hep-th↗

arXiv1998

Solutions of the Modified Chiral Model in (2+1) Dimensions

This paper deals with classical solutions of the modified chiral model on $R^{2+1}$. Such solutions are shown to correspond to products of various factor which we call time-dependent unitons. Then the problem of solving the system of second-order partial differential equations for the chiral field is reduced to solving a sequence of systems of first-order partial differential equations for the unitons.

hep-th↗

arXiv1995

Kinetics of phase ordering with topological textures

We study the role played by topological textures and antitextures during the phase ordering of a two-dimensional system described by the discretised nonlinear O(3) sigma model with purely dissipative dynamics. We identify and characterise two distinct mechanisms for the decay of the order parameter variations --- single texture unwinding, and topological charge annihilation. Our results show that while at early times after the quench, the annihilation process dominates, the unwinding processes become of comparable importance at later times. We calculate the correlations in the order parameter and in the topological charge density, and show that dynamical scaling is strongly violated due to the occurence of multiple length scales growing differently in time.

cond-mat↗