Joseph BERNSTEIN, Ossip SCHWARZMAN

Pages: 323 - 351

We prove that, for the irreducible complex crystallographic Coxeter group W, the
following conditions are equivalent: a) W is generated by reflections;
b) the analytic variety X/W is isomorphic to a weighted projective space.
The result is of interest, for example, in application to topological conformal...

Hailiang LIU

Pages: 441 - 466

The Korteweg de Vries (KdV) equation is well known as an approximation model
for small amplitude and long waves in different physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which...

Nadezda BAZUNOVA

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...

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...

Tatjana GRAMUSHNJAK, Peeter PUUSEMP

Pages: 55 - 65

Let n be an integer such that n 3 and Cm denote a cyclic group of order m . It
is proved that there exist exactly 17 non-isomorphic groups of order 22n+1
which can
be represented as a semidirect product (C2n × C2n ) C2. These groups are given by
generators and defining relations.

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.

Maido RAHULA, Vitali RETSNOI

Pages: 102 - 109

Total differentiation operators as linear vector fields, their flows, invariants and symmetries form the geometry of jet space. In the jet space the dragging of tensor fields
obeys the exponential law.
The composition of smooth maps induces a composition of jets in corresponding
jet spaces....

GEGENHASI, Xing-Biao HU

Pages: 183 - 192

M BRUSCHI

Pages: 205 - 210

New Cellular Automata associated with the Schroedinger discrete spectral problem
are derived. These Cellular Automata possess an infinite (countable) set of constants
of motion.

V ROSENHAUS

Pages: 255 - 270

We study local conservation laws and corresponding boundary conditions for the ptential Zabolotskaya-Khokhlov equation in (3+1)-dimensional case. We analyze an
infinite Lie point symmetry group of the equation, and generate a finite number of
conserved quantities corresponding to infinite symmetries...

F CALOGERO, J-P FRANCOISE

Pages: 231 - 254

We revisit an integrable (indeed, superintegrable and solvable) many-body model itroduced almost two decades ago by Gibbons and Hermsen and by Wojciechowski,
and we modify it so that its generic solutions are all isochronous (namely, completely
periodic with fixed period). We then show how this model...

Uma N IYER

Pages: 34 - 49

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.

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...

S N M RUIJSENAARS

Pages: 253 - 294

For positive parameters a+ and a- the commuting difference operators exp(ia±d/dz)
+ exp(2z/a), acting on meromorphic functions f(z), z = x + iy, are formally
self-adjoint on the Hilbert space H = L2
(R, dx). Volkov showed that they admit
joint eigenfunctions. We prove that the joint eigenfunctions...

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.

Jun-Xiao ZHAO, Chun-Xia LI, Xing-Biao HU

Pages: 238 - 245

A coupled Toda equation and its related equation are derived from 3-coupled bilinear
equations. The corresponding Bäcklund transformation and nonlinear superposition
formula are presented for the 3-coupled bilinear equations. As an application of the
results, solition solutions are derived. Besides,...

Zoran GRUJIC, Henrik KALISCH

Pages: 62 - 71

The derivative nonlinear Schrödinger equation is shown to be locally well-posed in
a class of functions analytic on a strip around the real axis. The main feature of the
result is that the width of the strip does not shrink in time. To overcome the derivative
loss, Kato-type smoothing results and...

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

E POLETAEVA

Pages: 141 - 147

We observe a correspondence between the zero modes of superconformal algebras
S (2, 1) and W(4) ([8]) and the Lie superalgebras formed by classical operators apearing in the Kähler and hyper-Kähler geometry.

Pascal REDOU

Pages: 136 - 140

Let F(Sn
) be the space of tensor densities on Sn
of degree . We consider this space
as an induced module of the nonunitary spherical series of the group SO0(n+1, 1) and
classify (so(n+1, 1), SO(n+1))-simple and unitary submodules of F(Sn
) as a function
of .

L. Martinez-Alonso, A B SHABAT

Pages: 229 - 242

We present a theory of compatible differential constraints of a hydrodynamic hierarchy
of infinite-dimensional systems. It provides a convenient point of view for studying
and formulating integrability properties and it reveals some hidden structures of the
theory of integrable systems. Illustrative...

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...

M SCHWARZ Jr

Pages: 65 - 77

In this work, we explain in what sense the generic level set of the constants of motion
for the periodic nonlinear Schrödinger equation is an infinite dimensional torus on
which each generalized nonlinear Schrödinger flow is reduced to straight line almost
periodic motion, and describe how neighboring...

A BELLOUQUID

Pages: 426 - 445

We establish the incompressible NavierStokes limit for the discrete velocity model of
the Boltzmann equation in any dimension of the physical space, for densities which rmain in a suitable small neighborhood of the global Maxwellian. Appropriately scaled
families solutions of discrete Boltzmann equation...

S DE LILLO, M C SALVATORI

Pages: 446 - 454

A one phase Stefan problem in nonlinear conduction is considered. The problem is
shown to admit a unique solution for small times. An exact solution is obtained which
is a travelling front moving with constant speed.

Barbara ABRAHAM-SHRAUNER

Pages: 1 - 9

The reduction of nonlinear ordinary differential equations by a combination of first
integrals and Lie group symmetries is investigated. The retention, loss or even gain
in symmetries in the integration of a nonlinear ordinary differential equation to a first
integral are studied for several examples....

Dmitry ROYTENBERG

Pages: 347 - 356

We compute the Poisson cohomology of the one-parameter family of SU(2)-covariant
Poisson structures on the homogeneous space S2
= CP1
= SU(2)/U(1), where SU(2)
is endowed with its standard PoissonLie group structure, thus extending the result
of Ginzburg [2] on the BruhatPoisson structure which...

Hervé LEBLOND

Pages: 325 - 346

We consider a wide class of model equations, able to describe wave propagation in
dispersive nonlinear media. The Korteweg-de Vries (KdV) equation is derived in this
general frame under some conditions, the physical meanings of which are clarified.
It is obtained as usual at leading order in some...

Ugurhan MU GAN, Fahd JRAD

Pages: 282 - 310

Starting from the second Painlevé equation, we obtain Painlevé type equations of
higher order by using the singular point analysis.

Hervé LEBLOND

Pages: 126 - 143

A new type of perturbative expansion is built in order to give a rigorous derivation
and to clarify the range of validity of some commonly used model equations. This
model describes the evolution of the modulation of two short and localized pulses,
fundamental and second harmonic, propagating together...

Atsushi NAKAMULA

Pages: 152 - 163

It is known that many integrable systems can be reduced from self-dual Yang-Mills
equations. The formal solution space to the self-dual Yang-Mills equations is given by
the so called ADHM construction, in which the solution space are graded by vector
spaces with dimensionality concerning topological...

Ken-ichi MARUNO, Wen-Xiu MA

Pages: 127 - 139

Hirota's bilinear technique is applied to some integrable lattice systems related to
the Bäcklund transformations of the 2DToda, Lotka-Volterra and relativistic LotkVolterra lattice systems, which include the modified Lotka-Volterra lattice system,
the modified relativistic Lotka-Volterra lattice system,...

Yi A LI

Pages: 99 - 105

We investigate linear stability of solitary waves of a Hamiltonian system. Unlike
weakly nonlinear water wave models, the physical system considered here is nonlinearly
dispersive, and contains nonlinearity in its highest derivative term. This results in
more detailed asymptotic analysis of the eigenvalue...

Yuri FEDOROV

Pages: 29 - 46

There is a wide class of integrable Hamiltonian systems on finite-dimensional coadjoint
orbits of the loop algebra ~gl(r) which are represented by r × r Lax equations with a
rational spectral parameter. A reduced complex phase space is foliated with open
subsets of Jacobians of regularized spectral...

Marek SZYDLOWSKI, Marek BIESIADA

Pages: 1 - 10

Qualitative approach to homogeneous anisotropic Bianchi class A models in terms
of dynamical systems reveals a hierarchy of invariant manifolds. By calculating the
Kovalevski Exponents according to Adler - van Moerbecke method we discuss how
algebraic integrability property is distributed in this...

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...

Adrian Constantin, Lotfi A. Zadeh

Pages: 0 - 0

Pages: -

Da Ruan

Pages: -

Adrian CONSTANTIN, Boris KOLEV

Pages: 471 - 474

For an integrable shallow water equation we describe a geometrical approach shoing that any two nearby fluid configurations are successive states of a unique flow
minimizing the kinetic energy.

Francesco TOPPAN

Pages: 518 - 533

The definition of "classical anomaly" is introduced. It describes the situation in which
a purely classical dynamical system which presents both a lagrangian and a hamitonian formulation admits symmetries of the action for which the Noether conserved
charges, endorsed with the Poisson bracket structure,...

Partha GUHA

Pages: 325 - 341

In this paper we study generalized classes of volume preserving multidimensional intgrable systems via NambuPoisson mechanics. These integrable systems belong to the
same class of dispersionless KP type equation. Hence they bear a close resemblance
to the self dual Einstein equation. All these dispersionless...

A SERGEEV

Pages: 229 - 255

Let A be an associative simple (central) superalgebra over C and L an invariant
linear functional on it (trace). Let a at
be an antiautomorphism of A such that
(at
)t
= (-1)p(a)
a, where p(a) is the parity of a, and let L(at
) = L(a). Then A admits
a nondegenerate supersymmetric invariant bilinear...

S N M RUIJSENAARS

Pages: 256 - 287

This is the second part of a series of papers dealing with an extensive class of anlytic difference operators admitting reflectionless eigenfunctions. In the first part, the
pertinent difference operators and their reflectionless eigenfunctions are constructed
from given "spectral data", in analogy...

M Yu RASULOVA

Pages: 235 - 239

The BBGKY's chain of quantum kinetic equations that describes the system of Bose
particles interacting by delta potential is solved by the operator method with the help
of nonlinear Schrödinger's equations. The solution of the chain is defined in terms of
the Bethe ansatz.

Pierre C SABATIER

Pages: 249 - 253

We use Lax equations to define a scattering problem on an infinite elbow shaped line
of the (x, t) plane. The evolution of scattering coefficients when the elbow is translated
in the plane shows how convenient scannings may reconstruct the solution V (x, t) of
the nonlinear equation associated to...

A E WINN

Pages: 294 - 299

An integrable interpolative (Pivotal) model for the (1 + 1)-dimensional Hyperbolic
Heisenberg and Hyperbolic sigma models is proposed and some solutions classifiable
by an integer winding number examined.

S N M RUIJSENAARS

Pages: 240 - 248

We present a scenario concerning the existence of a large class of reflectionless seladjoint analytic difference operators. In order to exemplify this scenario, we summarize
our results on reflectionless self-adjoint difference operators of relativistic CalogerMoser type.

Adam DOLIWA

Pages: 88 - 92

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