Pages: 7 - 12
At the quantum level of a bidimensional conformal model, the conformal symmtry is broken by the diffeomorphism anomaly and the conformal covariance is not maintained. Here we interpret geometrically this conformal covariance as an exact holomorphy condition on a two-dimensional Riemann surface on which...
Pages: 8 - 30
In this paper we study homogenization of quasi-linear partial differential equations of the form -div (a (x, x/h, Duh)) = fh on with Dirichlet boundary conditions. Here the sequence (h) tends to 0 as h and the map a (x, y, ) is periodic in y, monotone in and satisfies suitable continuity conditions....
Ismail Naci CANGÜL, Veli KURT, Yilmaz SIMSEK, Hong Kyung PAK, Seog-Hoon RIM
Pages: 8 - 14
The purpose of this paper is to consider q-Euler numbers and polynomials which are q-extensions of ordinary Euler numbers and polynomials by the computations of the p-adic q-integrals due to T. Kim, cf. [1, 3, 6, 12], and to derive the "complete sums for q-Euler polynomials" which are evaluated by using...
M.L. GANDARIAS, M.S. BRUZON
Pages: 8 - 12
We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation, which has the classical Boussinesq equation as an special case. We study the class of functions f(u) for which this equation admit either the classical or the...
A S HEGAZI, M MANSOUR
Pages: 9 - 18
In this paper, we define a new q-analogy of the Bernoulli polynomials and the Bernoulli numbers and we deduced some important relations of them. Also, we dduced a q-analogy of the Euler-Maclaurin formulas. Finally, we present a relation between the q-gamma function and the q-Bernoulli polynomials.
PGL LEACH, GP FLESSAS
Pages: 9 - 21
From time to time one finds claims in the literature that first integrals/invariants of Lagrangian systems are nonnoetherian. Such claims diminish the contribution of Noether in the topic of integrability. We provide an explicit demonstration of noethe- rian symmetries associated with the integrals which...
Harald GROSSE, Raimar WULKENHAAR
Pages: 9 - 20
We first review regularization methods based on matrix geometry which provide an ultraviolet cut-off for scalar fields respecting the symmetries. Sections of bundles over the sphere can be quantized, too. This procedure even allows to regularize supesymmetry without violating it. Recently, this work...
V ABRAMOV, O LIIVAPUU
Pages: 9 - 20
We propose a geometric approach to the BRST-symmetries of the Lagrangian of a topological quantum field theory on a four dimensional manifold based on the formalism of superconnections. Making use of a graded q-differential algebra, where q is a primitive N-th root of unity, we also propose a notion...
Octavian G MUSTAFA
Pages: 10 - 14
We prove that smooth solutions of the Degasperis-Procesi equation have infinite proagation speed: they loose instantly the property of having compact support.
Pages: 10 - 15
We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite time. Furthermore, we derive an explosion criterion for the equation and we give a sharp estimate...
K ANDRIOPOULOS, P G L LEACH
Pages: 10 - 23
The complete symmetry groups of systems of linear second order ordinary differential equations are considered in the context of the simple harmonic oscillator. One finds that in general the representation of the complete symmetry group is not unique and in the particular case of a four-dimensional system...
Pages: 11 - 20
A new integrable class of DaveyStewartson type systems of nonlinear partial diffrential equations (NPDEs) in 2+1 dimensions is derived from the matrix Kadomtsev Petviashvili equation by means of an asymptotically exact nonlinear reduction method based on Fourier expansion and spatio-temporal rescaling....
Tepper L. GILL, James LINDESAY, M.F. MAHMOOD, W.W. ZACHARY
Pages: 12 - 27
We report on a new formulation of classical relativistic Hamiltonian mechanics which is based on a proper-time implementation of special relativity using a transformation from observer proper-time, which is not invariant, to system proper-time which is a canonical contact transformation on extended phase-space....
Nicolas BURQ, Patrick GÉRARD, Nikolay TZVETKOV
Pages: 12 - 27
We discuss the wellposedness theory of the Cauchy problem for the nonlinear Schrödinger equation on compact Riemannian manifolds. New dispersive estimates on the linear Schrödinger group are used to get global existence in the energy space on arbirary surfaces and three-dimensional manifolds, generalizing...
Jehad O Alzabut
Pages: 13 - 21
The Banach fixed point theorem is used to prove the existence of a unique( w) periodic solution of a new type of nonlinear impulsive delay differential equation with a small parameter.
C WAFO SOH, F M MAHOMED
Pages: 13 - 20
The classical reduction of order for scalar ordinary differential equations (ODEs) fails for a system of ODEs. We prove a constructive result for the reduction of order for a system of ODEs that admits a solvable Lie algebra of point symmetries. Applications are given for the case of a system of two...
Peter A CLARKSON, Andrew N W HONE, Nalini JOSHI
Pages: 13 - 26
In this paper we present a method for deriving infinite sequences of difference equations containing well known discrete Painlevé equations by using the Bäcklund transformtions for the equations in the second Painlevé equation hierarchy.
Pages: 13 - 27
We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water’s free surface. Within the linear water wave theory, we show that there are no closed orbits for the water particles beneath the irrotational shallow water waves. Depending...
Stephen C ANCO, Thomas WOLF
Pages: 13 - 31
Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations Utx = f(U, Ut, Ux) for an N-component vector U(t, x) are considered. In each class we find all scalinhomogeneous equations admitting a higher symmetry of least...
Samir F. RADWAN
Pages: 13 - 34
The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate Du Fort Frankel scheme. The question of numerical...
Wilhelm FUSHCHYCH, Zoya SYMENOH
Pages: 13 - 22
We study symmetry properties of the Schrödinger equation with the potential as a new dependent variable, i.e., the transformations which do not change the form of the class of equations. We also consider systems of the Schrödinger equations with certain conditions on the potential. In addition we investigate...
Angel BALLESTEROS, Sergey CHUMAKOV
Pages: 13 - 17
The suq(2) algebra is shown to provide a natural dynamical algebra for some nonlnear models in Quantum Optics. Applications to the computation of eigenvalues and eigenvectors for the Hamiltonian describing second harmonics generation are proposed.
Robert CONTE, Micheline MUSETTE
Pages: 14 - 28
A birational transformation is one which leaves invariant an ordinary differential eqution, only changing its parameters. We first recall the consistent truncation which has allowed us to obtain the first degree birational transformation of Okamoto for the mater Painlevé equation P6. Then we improve...
E.V. FERAPONTOV, A.M. GRUNDLAND
Pages: 14 - 21
Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system
Pages: 15 - 27
By associating polynomials and power series expansions with sln(C) modules we dscribe the theory of Padé approximants in terms of tensor products of representations and interpret their recurrence relations algebraically. The treatment links with the theory of Hirota derivatives and discrete integrable...
R GOODALL, P G L LEACH
Pages: 15 - 26
Generalised symmetries and point symmetries coincide for systems of first-order odinary differential equations and are infinite in number. Systems of linear first-order ordinary differential equations possess a generalised rescaling symmetry. For the sytem of first-order ordinary differential equations...
Pages: 15 - 27
The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on Zp, we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple...
Vladimir DORODNITSYN, Roman KOZLOV
Pages: 16 - 50
In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation ut = (K(u)ux)x +Q(u). All special cases of K(u) and Q(u) that extend the symmetry group admitted by the differential equation are considered. This paper completes the...
Angel BALLESTEROS, Francisco J HERRANZ
Pages: 18 - 22
The two-photon algebra h6 is used to define an infinite class of N-particle Hamiltonian systems having (N -2) additional constants of the motion in involution. By constrution, all these systems are h6-coalgebra invariant. As a straightforward application, a new family of (quasi)integrable N-dimensional...
N BEN FRAJ, S OMRI
Pages: 19 - 33
We classify nontrivial deformations of the standard embedding of the Lie superalgebra K(1) of contact vector fields on the (1,1)-dimensional supercircle into the Lie supealgebra of superpseudodifferential operators on the supercircle. This approach leads to the deformations of the central charge induced...
Pages: 21 - 26
In this article, we generalize a construction of graded q-differential algebra with ternary differential satisfying the property d3 = 0 and q-Leibniz rule on the non-coordinate case, that is on the case where the differentials of generators of underlying algebra do not coincide with generators of bimodule...
Pages: 21 - 46
A new approach to the finite-gap property for the Heun equation is constructed. The relationship between the finite-dimensional invariant space and the spectral curve is clarified. The monodromies are calculated and are expressed as hyperelliptic integrals. Applications to the spectral problem for the...
S Yu SAKOVICH
Pages: 21 - 25
Integrability of differential constraints arising from the singularity analysis of two (1+1)-dimensional second-order evolution equations is studied. Two nonlinear ordnary differential equations are obtained in this way, which are integrable by quadrtures in spite of very complicated branching of their...
M MACEDA, J MADORE
Pages: 21 - 36
MC Nucci, P.G.L. Leach
Pages: 22 - 34
We apply singularity analysis to a caricature of the simplified multistrain model of Castillo-Chavez and Feng (J Math Biol 35 (1997) 629–656) for the transmission of tuberculosis and the coupled two-stream vector-based model of Feng and Velasco- Hern ?andez (J Math Biol 35 (1997) 523–544) to identify...
Pages: 22 - 33
A simple and general approach for calculating the elliptic finite-gap solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is based on the use of the finite-gap equations and the general representation of these solutions in the form of rational functions of the elliptic Weierstrass...
Pages: 22 - 33
We consider a lattice driven diffusive system withUq(su(2)) invariance in the bulk. Within the matrix product states approach the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra. Boundary processes amount to the appearance of parameter dependent...
R BEALS, D H SATTINGER, J SZMIGIELSKI
Pages: 23 - 27
Explicit formulas are given for the multi-peakon-antipeakon solutions of the Camassa Holm equation, and a detailed analysis is made of both short-term and long-term aspects of the interaction between a single peakon and single anti-peakon.
Pages: 23 - 40
We study the differential forms over the frame bundle of the based loop space. They are stochastics in the sense that we put over this frame bundle a probability measure. In order to understand the curvatures phenomena which appear when we look at the Lie bracket of two horizontal vector fields, we impose...
M. LAKSHMANAN, M. SENTHIL VELAN
Pages: 24 - 39
The Lie point symmetries associated with a number of (2 + 1)-dimensional generalizations of soliton equations are investigated. These include the Niznik Novikov Veselov equation and the breaking soliton equation, which are symmetric and asymmetric generalizations respectively of the KDV equation,...
T CERQUETELLI, N CICCOLI, M C NUCCI
Pages: 24 - 35
Realizations of four dimensional Lie algebras as vector fields in the plane are explcitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is described.
Sajid Ali, Fazal M Mahomed, Asghar Qadir
Pages: 25 - 35
We present the use of complex Lie symmetries in variational problems by defining a complex Lagrangian and considering its Euler-Lagrange ordinary differential equation. This Lagrangian results in two real “Lagrangians” for the corresponding system of partial differential equations, which satisfy Euler-Lagrange...
ANATOLIJ SAMOILENKO, LEON CHUA
Pages: 25 - 40
M A JAFARIZADEH, S BEHNIA
Pages: 26 - 41
We give a hierarchy of many-parameter families of maps of the interval [0, 1] with an invariant measure and using the measure, we calculate KolmogorovSinai entropy of these maps analytically. In contrary to the usual one-dimensional maps these maps do not possess period doubling or period-n-tupling...
C. BURDIK, S. POSTA, O NAVRATIL
Pages: 27 - 36
We study the exact solvable 3 × 3 matrix model of the type G2. We apply the construction similar to that one, which give the 2 × 2 matrix model. But in the studied case the construction does not give symmetric matrix potential. We conceive that the exact solvable 3 × 3 matrix potential model of the type...
Pages: 27 - 45
We define a Hopf C -algebra associated with an action of the quantum group SUq(1, 1) on a two-parameter quantum deformation of the unit disc, which has a left comodule structure over this Hopf C -algebra. Mathematics Subject Classification (1991). 81C05.
Alan K COMMON, Andrew N W HONE, Micheline MUSETTE
Pages: 27 - 40
By considering the Darboux transformation for the third order Lax operator of the Sawada-Kotera hierarchy, we obtain a discrete third order linear equation as well as a discrete analogue of the Gambier 5 equation. As an application of this result, we consider the stationary reduction of the fifth order...
Pages: 27 - 30
Given a steady and symmetric deep-water wave we prove that the surface profile and the vorticity distribution determine the wave motion completely throughout the fluid.
Shuyin Wu, Zhaoyang Yin
Pages: 28 - 49
In the paper, several problems on the periodic Degasperis-Procesi equation with weak dissipation are investigated. At first, the local well-posedness of the equation is established by Kato’s theorem and a precise blow-up scenario of the solutions is given. Then, several critera guaranteeing the blow-up...
I V BIKTASHEVA, V N BIKTASHEV
Pages: 28 - 34
Dynamics of spiral waves in perturbed two-dimensional autowave media can be dscribed asymptotically in terms of Aristotelean dynamics. We apply this general thory to the spiral waves in the Complex GinzburgLandau equation (CGLE). The RFs are found numerically. In this work, we study the dependence of...