Volume 14, Issue 3, October 2007

Delia Ionescu-Kruse

Pages: 311 - 320

We describe the physical hypothesis in which an approximate model of water waves is obtained. For an irrotational unidirectional shallow water flow, we derive the Camassa- Holm equation by a variational approach in the Lagrangian formalism.

Norbert Euler, Marianna Euler

Pages: 321 - 323

We report the recursion operators for a class of symmetry integrable evolution equa- tions of third order which admit a fourth-order integrating factor. Under some as- sumptions we obtain the complete list of equations, one of which is a special case of the Schwarzian Korteweg-de Vries equation.

Ahmed Fitouhi, Kamel Brahim

Pages: 324 - 340

In this paper we attempt to establish some tauberian theorems in quantum calculus. This constitutes the beginning of the study of the q-analogue of analytic theory of numbers which is the aim of a forthcoming paper.

Ferhan M. Atici, Paul W. Eloe

Pages: 341 - 352

The study of fractional q-calculus in this paper serves as a bridge between the fractional q-calculus in the literature and the fractional q-calculus on a time scale Tt0 = {t : t = t0 q n , n a nonnegative integer } âˆª {0}, where t0 âˆˆ R and 0 < q < 1. By use of time scale calculus notation, we find...

Julia Bernatska, Petro Holod

Pages: 353 - 374

We propose a general scheme for separation of variables in the integrable Hamilto- nian systems on orbits of the loop algebra sl(2, C) Ã— P (Î», Î» âˆ’1 ). In particular, we illus- trate the scheme by application to modified Kortewegâ€”de Vries (MKdV), sin(sinh)- Gordon, nonlinear Schr Ìˆodinger, and...

Fethi Bouzeffour

Pages: 375 - 388

A Whittaker-Shannon-Kotelâ€™nikov sampling theorem related to the Askey-Wilson functions is proved. Applications to finite continuous Askey-Wilson transform are given.

Yuri E. Gliklikh, Peter S. Zykov

Pages: 388 - 397

In A. Poltorak's concept, the reference frame in General Relativity is a certain manifold equipped with a connection. The question under consideration here is whether it is possible to join two events in the space-time by a time-like geodesic if they are joined by a geodesic of the reference frame connection...

Partha Guha

Pages: 398 - 429

In this paper we propose an Euler-Poincaré formalism of the Degasperis and Procesi (DP) equation. This is a second member of a one-parameter family of partial dif- ferential equations, known as b-field equations. This one-parameter family of pdes includes the integrable Camassa-Holm equation as a first...

Gazanfer Unal, Ismail Iyigunler, C Masood Khalique

Pages: 430 - 442

Necessary and sufficient conditions for the linearization of one-dimensional nonau- tonomous jump-diffusion stochastic differential equations are given. Stochastic inte- grating factor is introduced to solve the linear jump-diffusion stochastic differential equations. Closed form solutions to certain...

K S Govinder, P G L Leach

Pages: 443 - 461

The Emden-Fowler equation of index n is studied utilising the techniques of Lie and Painlev Ìe analysis. For general n information about the integrability of this equation is obtained. The link between these two types of analyses is explored. The special cases of n = âˆ’3, 2 are also examined. As a...

Robert Conte

Pages: 462 - 473

We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u â€²â€² + g1 (x)u â€² + g2 (x)u + g3 (x)u n + g4 (x) = 0, n real. Its physical applications range from the atomic Thomas-Fermi model to Emden gas dynamics...

Dimitrios A. Pinotsis

Pages: 474 - 493

We show that by deforming the Riemann-Hilbert (RH) formalism associated with certain linear PDEs and using the so-called dressing method, it is possible to derive in an algorithmic way nonlinear integrable versions of these equations. In the usual Dressing Method, one first postulates a matrix RH problem...