Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 14, Issue 3, October 2007
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 } ∪ {0}, where t0 ∈ R and 0 < q < 1. By use of time scale calculus notation,...
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) × P (λ, λ −1 ). In particular, we illus- trate the scheme by application to modified Korteweg—de Vries (MKdV), sin(sinh)- Gordon, nonlinear Schr ̈odinger,...
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 ́e 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 = −3, 2 are also examined....
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 ′′ + g1 (x)u ′ + g2 (x)u + g3 (x)u n + g4 (x) = 0, n real. Its physical applications range from the atomic Thomas-Fermi model...