905 articles

Jolanta GOLENIA, Anatoliy K PRYKARPATSKY, Yarema A PRYKARPATSKY

Pages: 73 - 87

An analog of Gelfand-Levitan-Marchenko integral equations for multi- dimensional Delsarte transmutation operators is constructed by means of studying their differentiageometric structure based on the classical Lagrange identity for a formally conjugated pair of differential operators. An extension of...

Carl M. Bender, E. Ben-Naim

Pages: 73 - 80

The nonlinear integral equation P(x) = dyw(y)P(y)P(x + y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions Pn(x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations...

Mats Ehrnstrom, Erik Wahlen

Pages: 74 - 86

This paper concerns linear standing gravity water waves on finite depth. We obtain qualitative and quantitative understanding of the particle paths within the wave.

H W BRADEN, K E FELDMAN

Pages: 74 - 85

We give a new derivation and characterisation of the generalised elliptic genus of Krichever-Höhn by means of a functional equation.

X B HU, P A CLARKSON

Pages: 75 - 83

A series of rational solutions are presented for an extended Lotka-Volterra eqution. These rational solutions are obtained by using Hirota's bilinear formalism and Bäcklund transformation. The crucial step is the use of nonlinear superposition fomula. The so-called extended Lotka-Volterra equation is...

WILHELM FUSHCHYCH, ROMAN POPOWYCH

Pages: 75 - 113

Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes equations are constructed.

R YAMILOV, D LEVI

Pages: 75 - 101

Conditions necessary for the existence of local higher order generalized symmetries and conservation laws are derived for a class of dynamical lattice equations with explicit dependence on the spatial discrete variable and on time. We explain how to use the obtained conditions for checking a given equation....

Daniel LARSSON, Gunnar SIGURDSSON, Sergei D SILVESTROV

Pages: 76 - 87

This paper explores the quasi-deformation scheme devised in [1, 3] as applied to the simple Lie algebra sl2(F) for specific choices of the involved parameters and underlying algebras. One of the main points of this method is that the quasi-deformed algebra comes endowed with a canonical twisted Jacobi...

R HERNÁNDEZ HEREDERO, D LEVI

Pages: 77 - 94

The Lie algebra L(h) of symmetries of a discrete analogue of the non-linear Schrödinger equation (NLS) is studied. A five-dimensional subspace of L(h), generated by both point and generalized symmetries, transforms into the five-dimensional point symmtry algebra L(0) of the NLS equation. We use the lowest...

Yuri N FEDOROV

Pages: 77 - 94

We show that the m-dimensional EulerManakov top on so (m) can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety ¯V(k, m), and present its Lax representation with a rational parameter. We also describe an integrable two-valued symplectic...

S GLADKOFF, A ALAIE, Y SANSONNET, M MANOLESSOU

Pages: 77 - 85

We present a numerical study of the nonlinear system of 4 0 equations of motion. The solution is obtained iteratively, starting from a precise point-sequence of the appropriate Banach space, for small values of the coupling constant. The numerical results are in perfect agreement with the main theoretical...

Tasawar Hayat, Herman Mambili-Mamboundou, Ebrahim Momoniat, Fazal M. Mahomed

Pages: 77 - 90

The influence of a magnetic field on the flow of an incompressible third grade electrically conducting fluid bounded by a rigid plate is investigated. The flow is induced due by the motion of a plate in its own plane with an arbitrary velocity. The solution of the equations of conservation of mass and...

Marek CZACHOR

Pages: 78 - 84

Reducible representations of CAR and CCR are applied to second quantization of Dirac and Maxwell fields. The resulting field operators are indeed operators and not operator-valued distributions. Examples show that the formalism may lead to a finite quantum field theory.

Artur SERGYEYEV, Jan A SANDERS

Pages: 78 - 85

We consider the CalogeroDegasperisIbragimovShabat (CDIS) equation and find the complete set of its nonlocal symmetries depending on the local variables and on the integral of the only local conserved density of the equation in question. The Lie algebra of these symmetries turns out to be a central...

O L de LANGE, J PIERRUS

Pages: 79 - 81

We consider the following question: Suppose part of the boundary of a cavity contaiing a gas is set into oscillation, the damping in the boundary being small. What is the nature of the oscillations in the gas? We treat the low-frequency limit (wavelength much greater than dimensions of the cavity). Experiment...

M.S. Bruzon, M. L. Gandarias, J. C. Camacho

Pages: 81 - 90

In this paper, the family of BBM equation with strong nonlinear dispersive B(m,n) is considered. We apply the classical Lie method of infinitesimals. The symmetry reductions are derived from the optimal system of subalgebras and lead to systems of ordinary differential equations. We obtain for special...

Junyi ZHU, Xianguo GENG

Pages: 81 - 89

The generalized dressing method is extended to variable-coefficient AKNS equations, including a variable-coefficient coupled nonlinear Schr¨odinger equation and a variablcoefficient coupled mKdV equation. A general variable-coefficient KP equation is proposed and decomposed into the two 1+1 dimensional...

S DE LILLO, V V KONOTOP

Pages: 82 - 87

We study statistical properties of inhomogeneous Burgers lattices which are solved by the discrete ColeHopf transformation. Using exact solutions we investigate effect of various kinds of noise on the dynamics of solutions.

P.G. ESTÉVEZ, E. CONDE, P.R. GORDOA

Pages: 82 - 114

This paper is an attempt to present and discuss at some length the Singular Manifold Method. This Method is based upon the Painlevé Property systematically used as a tool for obtaining clear cut answers to almost all the questions related with Nonlinear Partial Differential Equations: Lax pairs, Miura,...

Andrew RILEY, Ian A B STRACHAN

Pages: 82 - 94

Legendre transformations provide a natural symmetry on the space of solutions to the WDVV equations, and more specifically, between different Frobenius manifolds. In this paper a twisted Legendre transformation is constructed between solutions which define the corresponding dual Frobenius manifolds....

Roman GIELERAK, Robert RALOWSKI

Pages: 85 - 91

A class of involutive Wick algebras (called anyonic-type Wick algebras) is selected and some its elementary properties are described. In particular, the Fock representtions of the selected anyonic-type commutation relations are described. For the class of so-called r-yonic systems the question of the...

Evgenii M. VOROB'EV

Pages: 85 - 89

Computer-aided symbolic and graphic computation allows to make significantly easier both theoretical and applied symmetry analysis of PDE. This idea is illustrated by applying a special "Mathematica" package for obtaining conditional symmetries of the nonlinear wave equation ut = (u ux)x invariant or...

I G KOREPANOV, E V MARTYUSHEV

Pages: 86 - 98

We construct new topological invariants of three-dimensional manifolds which can, in particular, distinguish homotopy equivalent lens spaces L(7, 1) and L(7, 2). The invariants are built on the base of a classical (not quantum) solution of pentagon equation, i.e. algebraic relation corresponding to a...

Fabian BRAU

Pages: 86 - 96

We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schrödinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts are in Lp (Rn ) for some p > n (n = 1 or 3). An extension to confining...

Kenji KAJIWARA, Kinji KIMURA

Pages: 86 - 102

A q-difference analogue of the Painlevé III equation is considered. Its derivations, affine Weyl group symmetry, and two kinds of special function type solutions are discussed.

Eugen PAAL

Pages: 87 - 92

Deformation equation of a non-associative deformation in operad is proposed. Its integrability condition (the Bianchi identity) is considered. Algebraic meaning of the latter is explained.

David Henry

Pages: 87 - 95

We present a simple approach showing that Gerstner’s flow is dynamically possible: each particle moves on a circle, but the particles never collide and fill out the entire region below the surface wave.

Jyh-Hao LEE, Yen-Ching LEE, Chien-Chih LIN

Pages: 87 - 98

In this paper, we obtain some exact solutions of Derivative Reaction-Diffusion (DRD) system and, as by-products, we also show some exact solutions of DNLS via Hirota bilinearization method. At first, we review some results about two by two AKNS-ZS system, then introduce Hirota bilinearization method...

Adam DOLIWA

Pages: 88 - 92

The asymptotic lattices and their transformations are included into the theory of quadrilateral lattices.

Betti HARTMANN, Wojtek J ZAKRZEWSKI

Pages: 88 - 104

We study a model describing some aspects of the dynamics of biopolymers. The models involve either one or two finite chains with a number N of sites that represent the "units" of a biophysical system. The mechanical degrees of freedom of these chains are coupled to the internal degrees of freedom through...

R.Ya. MATSYUK

Pages: 89 - 97

Symmetries for variational problems are considered as symmetries of vector-valued exterior differential systems. This approach is applied to equations for the classical spinning particle.

Violeta TRETYNYK

Pages: 90 - 95

We search for hidden symmetries of two-particle equations with oscillator-equivalent potential proposed by Moshinsky with collaborators. We proved that these equations admit hidden symmetries and parasupersymmetries which enable easily to find the Hamiltonian spectra using algebraic methods.

Douglas BALDWIN, Willy HEREMAN

Pages: 90 - 110

The automation of the traditional Painlev´e test in Mathematica is discussed. The package PainleveTest.m allows for the testing of polynomial systems of nonlinear ordinary and partial differential equations which may be parameterized by arbitrary functions (or constants). Except where limited by memory,...

Ivan TSYFRA

Pages: 90 - 93

Operators of nonlocal symmetry are used to construct exact solutions of nonlinear heat equations. A method for finding of new classes of ansatzes reducing nonlinear wave equations to a systems of ordinary differential equations was suggested in [1]. This approach is based on nonlocal symmetry of differential...

Zoya SYMENOH

Pages: 90 - 95

The generalization of parasupersymmetric quantum mechanics generated by an arbitrary number of parasupercharges and characterized by an arbitrary order of paraquantization is given. The relations for parasuperpotentials are obtained. It is shown that parasuperpotentials can be explicitly expressed via...

T Hayat, Ebrahim Momoniat, Fazal M Mahomed

Pages: 91 - 104

This investigation deals with the mechanism of peristaltic transport of a non-Newtonian, incompressible and electrically conducting fluid with variable viscosity and an endoscope effects. The magnetic Reynolds number is taken to be small. The mechanical properties of the material are represented by the...

M. Calixto, V. Aldaya, F. F. Lopez-Ruiz, E. Sanchez-Sastre

Pages: 91 - 101

We extend the traditional formulation of Gauge Field Theory by incorporating the (non- Abelian) gauge group parameters (traditionally simple spectators) as new dynamical (nonlinearsigma- model-type) fields. These new fields interact with the usual Yang-Mills fields through a generalized minimal coupling...

D P MASON

Pages: 92 - 101

A group invariant solution for a steady two-dimensional jet is derived by considering a linear combination of the Lie point symmetries of Prandtl's boundary layer equations for the jet. Only two Lie point symmetries contribute to the solution and the ratio of the constants in the linear combination is...

Demosthenes ELLINAS, Elena P. PAPADOPOULOU, Yiannis G. SARIDAKIS

Pages: 93 - 99

A method of quantization of classical soliton cellular automata (QSCA) is put forward that provides a description of their time evolution operator by means of quantum cicuits that involve quantum gates from which the associated Hamiltonian describing a quantum chain model is constructed. The intrinsic...

Pavel KURASOV, Serguei NABOKO

Pages: 93 - 106

It is proven that the essential spectrum of any self-adjoint operator associated with the matrix differential expression

Peeter PUUSEMP

Pages: 93 - 101

It is proved that among the finite groups of order less than 32 only the tetrahedral group and the binary tetrahedral group are not determined by their endomorphism semigroups in the class of all groups.

I.G. KOREPANOV

Pages: 94 - 119

We give a review of some recent work on generalization of the Bethe ansatz in the case of 2 + 1-dimensional models of quantum field theory. As such a model, we consider one associated with the tetrahedron equation, i.e. the 2+1-dimensional generalization of the famous YangBaxter equation. We construct...

Misha FEIGIN

Pages: 95 - 136

We prove bispectral duality for the generalized CalogeroMoserSutherland systems related to configurations An,2(m), Cn(l, m). The trigonometric axiomatics of the BakerAkhiezer function is modified, the dual difference operators of rational Madonald type and the BakerAkhiezer functions related to both...

M F DAHL

Pages: 95 - 111

We study the complex Riccati tensor equation DcG + GCG - R = 0 on a geodesic c on a Riemannian 3-manifold. This non-linear equation appears in the study of Gaussian beams. Gaussian beams are asymptotic solutions to hyperbolic equations that at each time instant are concentrated around one point in space....

Daniel LARSSON, Sergei D SILVESTROV

Pages: 95 - 106

This paper is devoted to an extension of Burchnall-Chaundy theory on the inteplay between algebraic geometry and commuting differential operators to the case of q-difference operators.

Rafail K. GAZIZOV

Pages: 96 - 101

Properties of approximate symmetries of equations with a small parameter are discussed. It turns out that approximate symmetries form an approximate Lie algebra. A concept of approximate invariants is introduced and the algorithm of their calculating is proposed.

Octavian G Mustafa

Pages: 96 - 115

A new approach to the analysis of wave-breaking solutions to the generalized Camassa-Holm equation is presented in this paper. Introduction of a set of variables allows for solving the singularities. A continuous semigroup of dissipative solutions is also built. The solutions have non-increasing H1 energy...

J CHAVARRIGA, I A GARCIA

Pages: 96 - 105

The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G2 cosmologies. By using Darboux's theory in order to study ordinary differential equations...