Journal of Nonlinear Mathematical Physics

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....

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.

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.

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.

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 of...

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...

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, we show...

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...

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 be viewed as...

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...

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...

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...