Journal of Nonlinear Mathematical Physics

Volume 14, Issue 4, December 2007

1. Q->infinite limit of the quasitriangular WZW model

Pages: 494 - 526
We study the 'q-> infinite' limit of the q-deformation of the WZW model on a compact simple and simply connected target Lie group. We show that the commutation rela- tions of the 'q -> infinite' current algebra are underlied by certain affine Poisson structure on the group of holomorphic maps from the...

2. New solutions of a higher order wave equation of the KdV type

Pages: 527 - 533
In this paper we use the Painlev ́e analysis and study a special case of a water wave equation of the KdV type. More specifically, we use the Pickering algorithm [9] and obtain a new kind of solutions, which constitute of both algebraic and trigonometric (or hyperbolic) functions.

3. Mapping between the dynamic and mechanical properties of the relativistic oscillator and Euler free rigid body

Pages: 534 - 547
In this work we investigate a formal mapping between the dynamical properties of the unidimensional relativistic oscillator and the asymmetrical rigid top at a clas- sical level. We study the relativistic oscillator within Yamaleev’s interpretation of Nambu mechanics. Such interpretation is based on...

4. On the (3, N ) Maurer-Cartan equation

Mauricio ANGEL, Jaime CAMACARO, Rafael D ́IAZ
Pages: 548 - 569
Deformations of the 3-differential of 3-differential graded algebras are controlled by the (3, N ) Maurer-Cartan equation. We find explicit formulae for the coefficients appearing in that equation, introduce new geometric examples of N -differential graded algebras, and use these results to study N Lie...

5. On a construction of self-dual gauge fields in seven dimensions

Pages: 570 - 577
We consider gauge fields associated with a semisimple Malcev algebra. We construct a gauge-invariant Lagrangian and found a solution of modified Yang-Mills equations in seven dimensions.

6. Some spherical solutions of ideal magnetohydrodynamic equations

Pages: 578 - 588
Some spherical solutions of the ideal magnetohydrodynamic (MHD) equations are obtained from the method of the weak transversality method (WTM), which is based on Lie group theory. This analytical method makes use of the symmetry group of the MHD system in situations where the “classical” Lie approach...

7. On nonlocal symmetries of integrable three-field evolutionary systems

Pages: 589 - 611
Nonlocal symmetries for exactly integrable three-field evolutionary systems have been com- puted. Differentiation the nonlocal symmetries with respect to x gives a few hyperbolic systems for each evolution system. Zero curvature representations for all nonlocal systems and for some of the hyperbolic...

8. On a new technique to manufacture isochronous Hamiltonian systems: classical and quantal treatments

Pages: 612 - 636
We discuss a new technique to -modify real Hamiltonians so that they become isochronous while remaining real. Although the ω-modified Hamiltonians thereby obtained often yield, in the classical context, singular motions, we exhibit and inves- tigate simple examples when this does not (quite) happen....