Journal of Nonlinear Mathematical Physics

Volume 17, Issue 3, September 2010
Letter to Editor

1. Recursive Generation of Isochronous Hamiltonian Systems

V. K. Chandrasekar, A. Durga Devi, M. Lakshmanan
Pages: 251 - 256
We propose a simple procedure to identify the collective coordinate Q which is used to generate the isochronous Hamiltonian. The new isochronous Hamiltonian generates more and more isochronous oscillators, recursively.
Research Article

2. A Hamiltonian Action of the Schrödinger–Virasoro Algebra on a Space of Periodic Time-Dependent Schrödinger Operators in (1 + 1)-Dimensions

Claude Roger, Jérémie Unterberger
Pages: 257 - 279
Let be the space of Schrödinger operators in (1 + 1)-dimensions with periodic time-dependent potential. The action on 𝒮lin of a large infinite-dimensional reparametrization group SV with Lie algebra [8, 10], called the Schrödinger–Virasoro group and containing the Virasoro group, is proved to...
Research Article

3. Explicit Solution Processes for Nonlinear Jump-Diffusion Equations

Gazanfer Ünal, Hasret Turkeri, Chaudry Masood Khalique
Pages: 281 - 292
Recent studies have shown that the nonlinear jump-diffusion models give results which are in agreement with financial data. Here we provide linearization criteria together with transformations which linearize the nonlinear jump-diffusion models with compound Poisson processes. Furthermore, we introduce...
Research Article

4. On the Mapping of Jet Spaces

Václav Tryhuk, Veronika Chrastinová
Pages: 293 - 310
Any locally invertible morphism of a finite-order jet space is either a prolonged point transformation or a prolonged Lie's contact transformation (the Lie–Bäcklund theorem). We recall this classical result with a simple proof and moreover determine explicit formulae even for all (not necessarily...
Research Article

5. Diffraction of Electromagnetic Waves by a Layer Filled with a Kerr-Type Nonlinear Medium

Yury Shestopalov, Vasyl Yatsyk
Pages: 311 - 335
The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are developed. The diffraction problem is reduced to a singular boundary value...
Research Article

6. Magnetohydrodynamics's Type Equations Over Clifford Algebras

Igor Kondrashuk, Eduardo A. Notte-Cuello, Marko A. Rojas-Medar
Pages: 337 - 347
We study a system of equations modeling the stationary motion of incompressible electrical conducting fluid. Based on methods of Clifford analysis, we rewrite the system of magnetohydrodynamics fluid in the hypercomplex formulation and represent its solution in Clifford operator terms.
Research Article

7. Symmetry of osp(m|n) Spin Calogero–Sutherland Models

Kazuyuki Oshima
Pages: 349 - 356
We introduce osp(m|n) spin Calogero–Sutherland models and find that the models have the symmetry of osp(m|n) half-loop algebra or Yangian of osp(m|n) if and only if the coupling constant of the model equals to 2m−n−4.
Research Article

8. Discrete Multiscale Analysis: A Biatomic Lattice System

G. A. Cassatella Contra, D. Levi
Pages: 357 - 377
We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic excitations. We require that also the reduced equation be discrete....
Research Article

9. Integrability of Certain Deformed Nonlinear Partial Differential Equations

R. Sahadevan, L. Nalinidevi
Pages: 379 - 396
A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point of complete integrability, is presented. Following the procedure of Ablowitz, Kaup, Newell and Segur (AKNS) we find that the deformed version of Nonlinear Schrodinger equation, Hirota...
Research Article

10. Two New Solvable Dynamical Systems of Goldfish Type

F. Calogero
Pages: 397 - 414
Two new solvable dynamical systems of goldfish type are identified, as well as their isochronous variants. The equilibrium configurations of these isochronous variants are simply related to the zeros of appropriate Laguerre and Jacobi polynomials.