Journal of Nonlinear Mathematical Physics

Volume 10, Issue 1, February 2003

1. Noncentral Extensions as Anomalies in Classical Dynamical Systems

Jorge E SOLOMIN, Marcela ZUCCALLI
Pages: 1 - 9
A two cocycle is associated to any action of a Lie group on a symplectic manifold. This allows to enlarge the concept of anomaly in classical dynamical systems considered by F Toppan in [J. Nonlinear Math. Phys. 8, Nr. 3 (2001), 518­533] so as to encompass some extensions of Lie algebras related to...

2. On the Cauchy Problem for a Nonlinearly Dispersive Wave Equation

Zhaoyang YIN
Pages: 10 - 15
We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite time. Furthermore, we derive an explosion criterion for the equation and we give a sharp estimate...

3. A Heat Transfer with a Source: the Complete Set of Invariant Difference Schemes

Vladimir DORODNITSYN, Roman KOZLOV
Pages: 16 - 50
In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation ut = (K(u)ux)x +Q(u). All special cases of K(u) and Q(u) that extend the symmetry group admitted by the differential equation are considered. This paper completes...

4. The Poincaré­Nekhoroshev Map

Giuseppe GAETA
Pages: 51 - 64
We study a generalization of the familiar Poincaré map, first implicitely introduced by N N Nekhoroshev in his study of persistence of invariant tori in hamiltonian systems, and discuss some of its properties and applications. In particular, we apply it to study persistence and bifurcation of invariant...

5. Nonlinear Schrödinger, Infinite Dimensional Tori and Neighboring Tori

M SCHWARZ Jr
Pages: 65 - 77
In this work, we explain in what sense the generic level set of the constants of motion for the periodic nonlinear Schrödinger equation is an infinite dimensional torus on which each generalized nonlinear Schrödinger flow is reduced to straight line almost periodic motion, and describe how neighboring...

6. A Remark on Nonlocal Symmetries for the Calogero­Degasperis­Ibragimov­Shabat Equation

Artur SERGYEYEV, Jan A SANDERS
Pages: 78 - 85
We consider the Calogero­Degasperis­Ibragimov­Shabat (CDIS) equation and find the complete set of its nonlocal symmetries depending on the local variables and on the integral of the only local conserved density of the equation in question. The Lie algebra of these symmetries turns out to be a central...

7. On a q-Difference Painlevé III Equation: I. Derivation, Symmetry and Riccati Type Solutions

Kenji KAJIWARA, Kinji KIMURA
Pages: 86 - 102
A q-difference analogue of the Painlevé III equation is considered. Its derivations, affine Weyl group symmetry, and two kinds of special function type solutions are discussed.

8. On Frequencies of Small Oscillations of Some Dynamical Systems Associated with Root Systems

A M PERELOMOV
Pages: 103 - 109
In the paper by F Calogero and the author [Commun. Math. Phys. 59 (1978), 109­

9. On CP 1 and CP 2 Maps and Weierstrass Representations for Surfaces Immersed into Multi-Dimensional Euclidean Spaces

A M GRUNDLAND, W J ZAKRZEWSKI
Pages: 110 - 135
An extension of the classic Enneper­Weierstrass representation for conformally prametrised surfaces in multi-dimensional spaces is presented. This is based on low dimensional CP1 and CP2 sigma models which allow the study of the constant mean curvature (CMC) surfaces immersed into Euclidean 3- and...