Journal of Nonlinear Mathematical Physics

Volume 10, Issue 3, August 2003

1. On the Inverse Scattering Approach to the Camassa-Holm Equation

Adrian CONSTANTIN, Jonatan LENELLS
Pages: 252 - 255
A simple algoritm for the inverse scattering approach to the Camassa-Holm equation is presented.

2. Stationary Structures in Two-Dimensional Continuous Heisenberg Ferromagnetic Spin System

G M PRITULA, V E VEKSLERCHIK
Pages: 256 - 281
Stationary structures in a classical isotropic two-dimensional continuous Heisenberg ferromagnetic spin system are studied in the framework of the (2 + 1)-dimensional Landau­Lifshitz model. It is established that in the case of S(r, t) = S(r - vt) the Landau­Lifshitz equation is closely related to the...

3. On a q-Difference Painlevé III Equation: II. Rational Solutions

Kenji KAJIWARA
Pages: 282 - 303
Rational solutions for a q-difference analogue of the Painlevé III equation are consdered. A Determinant formula of Jacobi­Trudi type for the solutions is constructed.

4. Stability Analysis of Some Integrable Euler Equations for SO(n)

L FEHÉR, I MARSHALL
Pages: 304 - 317
A family of special cases of the integrable Euler equations on so(n) introduced by Manakov in 1976 is considered. The equilibrium points are found and their stability is studied. Heteroclinic orbits are constructed that connect unstable equilibria and are given by the orbits of certain 1-parameter subgroups...

5. q-Analogs of Classical 6-Periodicity: From Euler to Chebyshev

Boris A KUPERSHMIDT
Pages: 318 - 339
The sequence of period 6 starting with 1, 1, 0, -1, -1, 0 appears in many different disguises in mathematics. Various q-versions of this sequence are found, and their relations with Euler's pentagonal numbers theorem and Chebyshev polynomials are discussed. The motto on Cardinal Newman's tomb ought to...

6. Generalisations of the Laplace­Runge­Lenz Vector

P G L LEACH, G P FLESSAS
Pages: 340 - 423
The characteristic feature of the Kepler Problem is the existence of the so-called Laplace­Runge­Lenz vector which enables a very simple discussion of the properties of the orbit for the problem. It is found that there are many classes of problems, some closely related to the Kepler Problem and others...