In this paper we use deep ideas in complex geometry that proved to be very powerful
in unveiling the Polyakov measure on the moduli space of Riemann surfaces and lead
to obtain the partition function of perturbative string theory for 2, 3, 4 loops. Indeed
a geometrical interpretation of the conformal...
The Singular Manifold Method (SMM) is applied to an equation in 2 + 1 dimensions
 that can be considered as a generalization of the sine-Gordon equation. SMM
is useful to prove that the equation has two Painlevé branches and, therefore, it can
be considered as the modified version of an equation...
This paper investigates the nature of particle collisions for three-soliton solutions of
the Korteweg-de Vries (KdV) equation by describing mathematically the interaction
of soliton particles and generation of ghost particle radiation. In particular, it is
proven that a collision between any two soliton...
A solution of the KP-hierarchy can be given by the -function or the Baker function
associated to an element of the Grassmannian Gr(L2
)) consisting of some subspaces
of the space L2
) of square-integrable functions on the unit circle S1
. The Krichever
map associates an element W Gr(L2
An isochronous dynamical system is characterized by the existence of an open domain
of initial data such that all motions evolving from it are completely periodic with a fixed
period (independent of the initial data). Taking advantage of a recently introduced
trick, two new Hamiltonian classes of...
In this paper we further investigate some applications of Nambu mechanics in hydrdynamical systems. Using the Euler equations for a rotating rigid body Névir and
Blender [J. Phys. A 26 (1993), L1189L1193] had demonstrated the connection btween Nambu mechanics and noncanonical Hamiltonian mechanics....
Every smooth second-order scalar ordinary differential equation (ODE) that is solved
for the highest derivative has an infinite-dimensional Lie group of contact symmetries.
However, symmetries other than point symmetries are generally difficult to find and
use. This paper deals with a class of one-parameter...
We investigate weakly coupled semilinear parabolic systems in unbounded domains in
with polynomial nonlinearities. Three sufficient conditions are presented to
ensure the stability of the zero solution with respect to non-negative H2
We consider the propagation of TE-polarized electromagnetic waves in cylindrical
dielectric waveguides of circular cross section filled with lossless, nonmagnetic, and
isotropic medium exhibiting a local Kerr-type dielectric nonlinearity. We look for
axially-symmetric solutions and reduce the problem...
A recent paper by Karasu (Kalkanli) and Yildirim (Journal of Nonlinear Mathematical
Physics 9 (2002) 475-482) presented a study of the Kepler-Ermakov system in the
context of determining the form of an arbitrary function in the system which was
compatible with the presence of the sl(2, R) algebra...