Journal of Nonlinear Mathematical Physics

Volume 13, Issue 3, August 2006
Research Article

1. A note on q-Bernoulli numbers and polynomials

Taekyun Kim, A.S. Hegazi, M. Mansour
Pages: 315 - 322
Recently, B. A. Kupershmidt have constructed a reflection symmetries of q-Bernoulli polynomials (see [9]). In this paper we give another construction of a q-Bernoulli polynomials, which form Barnes' multiple Bernoulli polynomials at q = 1, cf. [1, 13,14]. By using q-Volkenborn integration, we can also...
Research Article

2. Chevalley's theorem for the complex crystallographic groups

Joseph Bernstein, Ossip Schwarzman
Pages: 323 - 351
We prove that, for the irreducible complex crystallographic Coxeter group W, the following conditions are equivalent: a) W is generated by reflections; b) the analytic variety X/W is isomorphic to a weighted projective space. The result is of interest, for example, in application to topological conformal...
Research Article

3. Bihamiltonian Equations on Polynomial Virasoro

Paolo Casati, Giovanni Ortenzi
Pages: 352 - 364
We present and study bihamiltonian equations of Euler type which include a n
Research Article

4. Feynman-Jackson integrals

Rafael Díaz, Eddy Pariguan
Pages: 365 - 376
We introduce perturbative Feynman integrals in the context of q-calculus generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide analytic as well as combinatorial interpretations for the Feynman-Jackson integrals.
Research Article

5. Nonlocal Symmetries and the Complete Symmetry Group of 1 + 1 Evolution Equations

S.M. Myeni, P.G.L. Leach
Pages: 377 - 392
The complete symmetry group of a 1 + 1 linear evolution equation has been demon- strated to be represented by the six-dimensional Lie algebra of point symmetries sl(2, R)?s W , where W is the three-dimensional Heisenberg-Weyl algebra. The infinite number of solution symmetries does not play a role in...
Research Article

6. Riemann Invariants and Rank-k Solutions of Hyperbolic Systems

A.M. Grundland, B. Huard
Pages: 393 - 419
In this paper we employ a “direct method” to construct rank-k solutions, express- ible in Riemann invariants, to hyperbolic system of first order quasilinear differential equations in many dimensions. The most important feature of our approach is the analysis of group invariance properties of these solutions...
Research Article

7. Vectorial Regularization and Temporal Means in Keplerian Motion

Daniel Condurache, Vladimir Martinusi
Pages: 420 - 440
We study the well-known Kepler’s problem by introducing a new vectorial regularization. This helps deduce Kepler’s equations by a simple and unified method. Some integral temporal means are also obtained by means of this regularization. The vectorial eccentricity plays a fundamental part in this approach.
Research Article

8. Wave Breaking in a Class of Nonlocal Dispersive Wave Equations

Hailiang Liu
Pages: 441 - 466
The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in different physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which also...