Pages: 467 - 478
We construct a Lax operator for the G2-Calogero-Moser model by means of a double
reduction procedure. In the first reduction step we reduce the A6-model to a Bmodel with the help of an embedding of the B3-root system into the A6-root system
together with the specification of certain coupling constants....
Pages: 479 - 483
In this paper, we get an asymptotic expansion of the q-gamma function q(x). Also, we deduced
q-analogues of Gauss' multiplication formula and Legendre's relation which give the known results
when q tends to 1.
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: 492 - 506
This paper aims to study the q-wavelets and the q-wavelet transforms, using only the
q-Jackson integrals and the q-cosine Fourier transform, for a fix q ]0, 1[. For this
purpose, we shall attempt to extend the classical theory by giving their q-analogues.
Pages: 507 - 515
Considering the kinematics of the moving frame associated with a constant mean cuvature surface immersed in S3
we derive a linear problem with the spectral parameter
corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to
the radius R of the sphere S3
. The application...
Pages: 516 - 522
In this paper we want to characterize nonlinear differential equations that describe
processes allowing a localization operation in each subdomain of domain in which we
consider the process. We formulate this localization condition by means of visual reresentations and give this operation a mathematical...
Pages: 523 - 534
We investigate the first cohomology space associated with the embedding of the Lie
superalgebra K(2) of contact vector fields on the (1,2)-dimensional supercircle S1|2
the Lie superalgebra SDO(S1|2
) of superpseudodifferential operators with smooth
coefficients. Following Ovsienko and Roger,...
Pages: 535 - 548
We analyse the classical model of competition between three species studied by May
and Leonard (SIAM J Appl Math 29 (1975) 243-256) with the approaches of singlarity analysis and symmetry analysis to identify values of the parameters for which
the system is integrable. We observe some striking relations...
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: 566 - 583
In this paper, we study some remarkable spaces of Sq,(Rq,+) space of the q-tempered
distribution introduced by M.A. Olshanetsky and V.B.K. Rogov , namely the
q-analogue of the pseudo-measure FqL
(Rq,+), the q-function of the positive type
FqM , and we give a q-version of the Bochner-Shwartz theorem...
Pages: 584 - 611
We obtain isomonodromic transformations for Heun's equation by generalizing the
Darboux transformation, and we find pairs and triplets of Heun's equation which have
the same monodromy structure. By composing generalized Darboux transformations,
we establish a new construction of the commuting operator...
Pages: 612 - 622
The provenance of Type II hidden point symmetries of differential equations reduced
from nonlinear partial differential equations is analyzed. The hidden symmetries are
extra symmetries in addition to the inherited symmetries of the differential equations
when the number of independent and dependent...