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...
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...
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...
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...
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
be represented as a semidirect product (C2n × C2n ) C2. These groups are given by
generators and defining relations.
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.
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
Pages: 183 - 192
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
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...
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...
Pages: 34 - 49
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.
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...
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...
Pages: 147 - 152
Pages: 240 - 252
We consider a longrange homogeneous chain where the local variables are the geerators of the direct sum of N e(3) interacting Lagrange tops. We call this classical
integrable model rational "Lagrange chain" showing how one can obtain it starting
from su(2) rational Gaudin models. Moreover we construct...
Pages: 178 - 208
Separable coordinate systems are introduced in complex and real four-dimensional
flat spaces. We use maximal Abelian subgroups to generate coordinate systems with
a maximal number of ignorable variables. The results are presented (also graphically)
in terms of subgroup chains. Finally the explicit...
Pages: 162 - 169
In this paper we are interested in developments of the elliptic functions of Jacobi.
In particular a trigonometric expansion of the classical theta functions introduced
by the author (Algebraic methods and q-special functions, C.R.M. Proceedings and
Lectures Notes, A.M.S., vol 22, Providence, 1999,...
Pages: 170 - 177
A huge family of separable potential perturbations of integrable billiard systems and
the Jacobi problem for geodesics on an ellipsoid is given through the Appell hypegeometric functions F4 of two variables, leading to an interesting connection between
two classical theories: separability in HamiltonJacobi...
Pages: 31 - 52
A concept of strong necessary conditions for extremum of functional has been aplied for analysis an existence of dual equations for a system of two nonlinear Partial
Differential Equations (PDE) in 1+1 dimensions. We consider two types of the dual
equations: the Bäcklund transformations and the Bogomolny...
Pages: 1 - 9
The article is devoted to studying the Millionshtchikov closure model (a particular
case of a model introduced by Oberlack ) for isotropic turbulence dynamics which
appears in the context of the theory of the von K´arm´an-Howarth equation. We write
the model in an abstract form that enables us...
Pages: 315 - 326
This article displays examples of planar isochronous systems and discuss the new
techniques found by F. Calogero with these examples. A sufficient condition is found
to keep track of some periodic orbits for perturbations of isochronous systems.
Pages: 404 - 411
The concept of measurement in classical scattering is interpreted as an overlap of a
particle packet with some area in phase space that describes the detector. Considering
that usually we record the passage of particles at some point in space, a common
detector is described e.g. for one-dimensional...
Pages: 253 - 265
We compute the spectrum of the trigonometric Sutherland spin model of BCN type
in the presence of a constant magnetic field. Using Polychronakos's freezing trick, we
derive an exact formula for the partition function of its associated HaldaneShastry
Pages: 184 - 201
We discuss a method of solving nth
order scalar ordinary differential equations by
extending the ideas based on the Prelle-Singer (PS) procedure for second order ordnary differential equations. We also introduce a novel way of generating additional
integrals of motion from a single integral. We illustrate...
Pages: 244 - 252
We study a potential introduced by Darboux to describe conjugate nets, which within
the modern theory of integrable systems can be interpreted as a -function. We
investigate the potential using the nonlocal ¯-dressing method of Manakov and Zkharov and we show that it can be interpreted as the Fredholm...
Pages: 212 - 227
We consider the cubic and quartic Hénon-Heiles Hamiltonians with additional inverse
square terms, which pass the Painlevé test for only seven sets of coefficients. For all
the not yet integrated cases we prove the singlevaluedness of the general solution. The
seven Hamiltonians enjoy two properties:...
Pages: 280 - 301
We re-express the quantum Calogero-Sutherland model for the Lie algebra E6 and the
particular value of the coupling constant = 1 by using the fundamental irreducible
characters of the algebra as dynamical variables. For that, we need to develop a
systematic procedure to obtain all the Clebsch-Gordan...
Pages: 138 - 145
We prove reality of the spectrum for a class of PT - symmetric, non self-adjoint
quantum nonlinear oscillators of the form H = p2
+ P(q) + igQ(q). Here P(q) is an
even polynomial of degree 2p positive at infinity, Q(q) an odd polynomial of degree
2r - 1, and the conditions p > 2r, |g| < R for some...
Pages: 302 - 314
The phenomenon of steady streaming, or acoustic streaming, is an important phyical phenomenon studied extensively in the literature. Its mathematical formulation
involves the Navier-Stokes equations, and due to the complexity of these equations is
usually studied heuristically using formal perturbation...
Pages: 372 - 379
Berger and Stassen reviewed skein relations for link invariants coming from the simple
Lie algebras g. They related the invariants with decomposition of the tensor square of
the g-module V of minimal dimension into irreducible components. (If V V
should also consider the decompositions of...
Pages: 549 - 565
The standard embedding of the Lie algebra V ect(S1
) of smooth vector fields on
the circle V ect(S1
) into the Lie algebra D(S1
) of pseudodifferential symbols on
identifies vector field f(x)
x V ect(S1
) and its dual as (f(x)
x ) = f(x)
) = u(x)-2
. The space of symbols can...
Pages: 484 - 491
We consider a symmetric, steady, and periodic water wave. It is shown that a locally
vanishing vertical velocity component implies a flat or oscillating surface profile.
Pages: 435 - 460
Pages: 534 - 548
The goal of this survey article is to explain the up-to-date state of the theory of
Lp - Lq decay estimates for wave equations with time-dependent coefficients. We
explain the influence of oscillations in the coefficients by using a precise classification.
Moreover, we will see how mass and dissipation...
Pages: 521 - 533
We survey recent results on well-posedness, blow-up phenomena, lifespan and global
existence for the Camassa-Holm equation. Results on weak solutions are also consiered.
Pages: 138 - 144
We derive and discuss equations of motion of infinitesimal affinely-rigid body moving
in Riemannian spaces. There is no concept of extended rigid and affinely rigid body in
a general Riemannian space. Therefore the gyroscopes with affine degrees of freedom
are described as moving bases attached to...
Pages: 179 - 184
We give a short review of recent results on L2
-cohomology of infinite configuration
spaces equipped with Poisson measures.
Pages: 350 - 360
We consider the general properties of the quasispecies dynamical system from the
standpoint of its evolution and stability. Vector field analysis as well as spectral
properties of such system have been studied. Mathematical modeling of the system
under consideration has been performed.
Pages: 276 - 288
This paper deals with a method for the linearization of nonlinear autonomous diferential equations with a scalar nonlinearity. The method consists of a family of
approximations which are time independent, but depend on the initial state. The
family of linearizations can be used to approximate the derivative...
Pages: 376 - 398
The set of systems of differential equations that are in normal form with respect to
a particular linear part has the structure of a module of equivariants, and is best
described by giving a Stanley decomposition of that module. In this paper Groebner
basis methods are used to determine a Groebner...
Pages: 199 - 207
A solution of the KP-hierarchy can be given by the -function or the Baker function
associated to an element of the Grassmannian Gr(L2
)) consisting of some subspaces
of the space L2
) of square-integrable functions on the unit circle S1
. The Krichever
map associates an element W Gr(L2
Pages: 180 - 198
This paper investigates the nature of particle collisions for three-soliton solutions of
the Korteweg-de Vries (KdV) equation by describing mathematically the interaction
of soliton particles and generation of ghost particle radiation. In particular, it is
proven that a collision between any two soliton...
Pages: 123 - 133
We examine the classical model of two competing species for integrability in terms
of analytic functions by means of the Painlevé analysis. We find that the governing
equations are integrable for certain values of the essential parameters of the system.
We find that, for all integrable cases with...
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...
Pages: 149 - 165
We present an extension of a family of second-order integrable mappings to the case
where the variables do not commute. In every case we introduce a commutation
rule which is consistent with the mapping evolution. Through the proper ordering of
variables we ensure the existence of an invariant in...
Pages: 194 - 208
Möbius invariant versions of the discrete Darboux, KP, BKP and CKP equations are
derived by imposing elementary geometric constraints on an (irregular) lattice in a
three-dimensional Euclidean space. Each case is represented by a fundamental theorem
of plane geometry. In particular, classical theorems...
Pages: 333 - 347
A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy...
Pages: 365 - 382
In this paper we compute first integrals of nonlinear ordinary differential equations using the extended Prelle-Singer method, as formulated by Chandrasekar et al in J. Math. Phys. 47 (2), 023508, (2006). We find a new first integral for the Painlev´e-Gambier XXII equation. We also derive the first integrals...