Solitons in the Yakushevich model of DNA beyond the contact approximation

The Yakushevich model of DNA torsion dynamics supports soliton solutions, which are supposed to be of special interest for DNA transcription. In the discussion of the model, one usually adopts the approximation $\ell_0 \to 0$, where $\ell_0$ is a parameter related to the equilibrium distance between bases in a Watson-Crick pair. Here we analyze the Yakushevich model without $\ell_0 \to 0$. The model still supports soliton solutions indexed by two winding numbers $(n,m)$; we discuss in detail the fundamental solitons, corresponding to winding numbers (1,0) and (0,1) respectively

Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras

Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear variable-coefficient evolution equations, both in 1+1 dimensions and in 2+1 dimensions, which possess higher-degree polynomial-in-time dependent symmetries. The theory also provides a kind of new realisation of graded Lie algebras. Some illustrative examples are given.Comment: 11 pages, latex, to appear in J. Phys. A: Math. Ge

A New Nonlinear Liquid Drop Model. Clusters as Solitons on The Nuclear Surface

By introducing in the hydrodynamic model, i.e. in the hydrodynamic equations and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equation (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by the ratio of the square amplitudes in the two minima.Comment: 27 pages, LateX, 8 figures, Submitted J. Phys. G: Nucl. Part. Phys., PACS: 23.60.+e, 21.60.Gx, 24.30.-v, 25.70.e

Invariant solutions of the supersymmetric sine-Gordon equation

A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to the coefficients of the various powers of the anticommuting independent variables. Next, we consider the super-sine-Gordon equation expressed in terms of a bosonic superfield involving anticommuting independent variables. In each case, a Lie (super)algebra of symmetries is determined and a classification of all subgroups having generic orbits of codimension 1 in the space of independent variables is performed. The method of symmetry reduction is systematically applied in order to derive invariant solutions of the supersymmetric model. Several types of algebraic, hyperbolic and doubly periodic solutions are obtained in explicit form.Comment: 27 pages, major revision, the published versio

Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases

We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.Comment: 18 pages, Latex, Revtex

Completely integrable models of non-linear optics

The models of the non-linear optics in which solitons were appeared are considered. These models are of paramount importance in studies of non-linear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency, and parametric interaction of three waves. At the present time there are a number of the theories based on completely integrable systems of equations, which are both generations of the original known models and new ones. The modified Korteweg-de Vries equation, the non- linear Schrodinger equation, the derivative non-linear Schrodinger equation, Sine-Gordon equation, the reduced Maxwell-Bloch equation, Hirota equation, the principal chiral field equations, and the equations of massive Thirring model are gradually putting together a list of soliton equations, which are usually to be found in non-linear optics theory.Comment: Latex, 17 pages, no figures, submitted to Pramana

Non-singular screw dislocations as the Coulomb gas with smoothed out coupling and the renormalization of the shear modulus

A field theory is developed for a thermodynamical description of array of parallel non-singular screw dislocations in elastic cylinder. The partition function of the system is considered in the functional integral form. Self-energy of the dislocation cores is chosen in the form suggested by the gauge-translational model of non-singular screw dislocation. It is shown that the system of the dislocations is equivalent to the two-dimensional Coulomb gas. The coupling potential is prevented from a short-distance divergency since the core energies are taken into account. Two-point correlation functions of the stress components are obtained. Renormalization of the shear modulus caused by the presence of the dislocations is studied in the approximation of non-interacting dislocation dipoles. It is demonstrated that the finite size of the dislocation cores results in a modification of the renormalization law.Comment: 20 pages, LaTe

Move over Nelly: lessons from 30 years of employment-based initial teacher education in England

Recruiting, preparing and retaining high-quality teachers are recurrent themes of local, national and international education agendas. Traditional university-led forms of teacher education continue to be challenged, and defended, as nations strive to secure a teaching force equipped to achieve high-quality learning outcomes for all students. One commonly adopted policy solution has been the diversification of teacher preparation routes: the alternative certification agenda. In this article, we examine the entire history of one alternative route in place in England from 1997 to 2012, the Graduate Teacher Programme. Using one example of an employment-based programme, we argue that opportunities to engineer innovative and creative spaces in the face of the current teacher preparation reform agenda need to be seized. This case study, which is contextualised in both the international debates about alternative teacher certification routes and the current policy agenda in England, demonstrates the extent to which successive administrations have failed to learn from the lessons of the past in the rush to recycle policies and claim them as their own

Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models

The main purpose of this paper is to extend results, which have been obtained previously to describe the classical scattering of solitons with integrable defects of type I, to include the much larger and intricate collection of finite-gap solutions defined in terms of generalised theta functions. In this context, it is generally not feasible to adopt a direct approach, via ansätze for the fields to either side of the defect tuned to satisfy the defect sewing conditions. Rather, essential use is made of the fact that the defect sewing conditions themselves are intimately related to Bäcklund transformations in order to set up a strategy to enable the calculation of the field on one side by suitably transforming the field on the other side. The method is implemented using Darboux transformations and illustrated in detail for the sine-Gordon and KdV models. An exception, treatable by both methods, indirect and direct, is provided by the genus 1 solutions. These can be expressed in terms of Jacobi elliptic functions, which satisfy a number of useful identities of relevance to this problem. There are new features to the solutions obtained in the finite-gap context but, in all cases, if a (multi)soliton limit is taken within the finite-gap solutions previously known results are recovered