Journal of Nonlinear Mathematical Physics

Volume 11, Issue 2, May 2004
Research Article

1. Geometrical Formulation of the Conformal Ward Identity

Mohamed Kachkachi
Pages: 141 - 150
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...
Research Article

2. A Variational Approach to the Stability of Periodic Peakons

Jonatan Lenells
Pages: 151 - 163
The peakons are peaked traveling wave solutions of an integrable shallow water eqution. We present a variational proof of their stability.
Research Article

3. A Generalization of the Sine-Gordon Equation to 2 + 1 Dimensions

P.G. Estévez, J. Prada
Pages: 164 - 179
The Singular Manifold Method (SMM) is applied to an equation in 2 + 1 dimensions [13] 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...
Research Article

4. Soliton Collisions and Ghost Particle Radiation

Hiêú D. Nguyêñ
Pages: 180 - 198
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...
Research Article

5. The Krichever Map and Automorphic Line Bundles

Min Ho Lee
Pages: 199 - 207
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 (S1 )) consisting of some subspaces of the space L2 (S1 ) of square-integrable functions on the unit circle S1 . The Krichever map associates an element W Gr(L2 (S1 ))...
Research Article

6. Two New Classes of Isochronous Hamiltonian Systems

Francesco Calogero
Pages: 208 - 222
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 such...
Research Article

7. Applications of Nambu Mechanics to Systems of Hydrodynamical Type II

Partha Guha
Pages: 223 - 232
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....
Research Article

8. Self-Invariant Contact Symmetries

Peter E. Hydon
Pages: 233 - 242
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...
Research Article

9. Stable Equilibria to Parabolic Systems in Unbounded Domains

Joachim Escher, Zhaoyang Yin
Pages: 243 - 255
We investigate weakly coupled semilinear parabolic systems in unbounded domains in R2 or R3 with polynomial nonlinearities. Three sufficient conditions are presented to ensure the stability of the zero solution with respect to non-negative H2 -perturbations.
Research Article

10. Integral Equation Approach for the Propagation of TE-Waves in a Nonlinear Dielectric Cylindrical Waveguide

Y. Smirnov, H.W. Schürmann, Y. Shestopalov
Pages: 256 - 268
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...

11. The Lie Algebra sl(2, R) and so-called Kepler-Ermakov Systems

P.G.L. Leach, Ayse Karasu Kalkanli
Pages: 269 - 275
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 characteristic...