Journal of Nonlinear Mathematical Physics

Volume 13, Issue 4, November 2006

1. G2-Calogero-Moser Lax operators from reduction

Andreas Fring, Nenad Manojlovic
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....

2. An asymptotic expansion of the q-gamma function q(x)

M Mansour
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.

3. A unique continuation principle for steady symmetric water waves with vorticity

Mats Ehrnström
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.

4. Wavelet Transforms in Quantum Calculus

Ahmed Fitouhi, Néji Bettaibi
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.

5. A geometric interpretation of the spectral parameter for surfaces of constant mean curvature

J L Cieslinski
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...

6. On Nonlinear Differential Equations That Describe Localized Processes

Vladimir P Burskii
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...

7. On the Cohomology of the Lie Superalgebra of Contact Vector Fields on S1|2

B. Agrebaoui, N. Ben Fraj, S. Omri
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 in the Lie superalgebra SDO(S1|2 ) of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger,...

8. Analytic Behaviour of Competition among Three Species

Pgl Leach, J Miritzis
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...

9. Vect(S1) Action on Pseudodifferential Symbols on S1 and (Noncommutative) Hydrodynamic Type Systems

Partha Guha
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 S1 identifies vector field f(x) x V ect(S1 ) and its dual as (f(x) x ) = f(x) (u(x)dx2 ) = u(x)-2 . The space of symbols can...

10. Distribution of positive type in Quantum Calculus

Akram Nemri
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 [14], 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...

11. The Heun equation and the Calogero-Moser-Sutherland system V: generalized Darboux transformations

Kouichi Takemura
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...

12. Provenance of Type II hidden symmetries from nonlinear partial differential equations

Barbara Abraham-shrauner, Keshlan S Govinder
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...