Volume 10, Issue 1, February 2003
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...
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...
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...
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...
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...
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...
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
Pages: 103 - 109
In the paper by F Calogero and the author [Commun. Math. Phys. 59 (1978), 109
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
sigma models which allow the study of the constant mean
curvature (CMC) surfaces immersed into Euclidean 3- and...