Journal of Nonlinear Mathematical Physics

Volume 10, Issue 4, November 2003

1. Hk Metrics on the Diffeomorphism Group of the Circle

Adrian CONSTANTIN, B KOLEV
Pages: 424 - 430
Each Hk inner product, k N, endows the diffeomorphism group of the circle with a Riemannian structure. For k 1 the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of geodesics holds.

2. Multiple Hamiltonian Structures and Lax Pairs for Bogoyavlensky­Volterra Systems

Stelios P KOUZARIS
Pages: 431 - 450
Results on the Volterra model which is associated to the simple Lie algebra of type An are extended to the Bogoyavlensky­Volterra systems of type Bn, Cn and Dn. In paticular we find Lax pairs, Hamiltonian and Casimir functions and multi-Hamiltonian structures. Moreover, we investigate recursion operators,...

3. Dirac Reduction Revisited

Krzysztof MARCINIAK, Maciej BLASZAK
Pages: 451 - 463
The procedure of Dirac reduction of Poisson operators on submanifolds is discussed within a particularly useful special realization of the general Marsden-Ratiu redution procedure. The Dirac classification of constraints on `first-class' constraints and `second-class' constraints is reexamined.

4. On Vortex Solutions and Links between the Weierstrass System and the Complex Sine-Gordon Equations

P BRACKEN, P P GOLDSTEIN, A M GRUNDLAND
Pages: 464 - 486
The connection between the complex Sine and Sinh-Gordon equations associated with a Weierstrass type system and the possibility of construction of several classes of multivortex solutions is discussed in detail. We perform the Painlevé Test and analyse the possibility of deriving the Bäcklund transformation...

5. A Method for q-Calculus

Thomas ERNST
Pages: 487 - 525
We present a notation for q-calculus, which leads to a new method for computtions and classifications of q-special functions. With this notation many formulas of q-calculus become very natural, and the q-analogues of many orthogonal polynomals and functions assume a very pleasant form reminding directly...

6. Soliton Solutions of the N = 2 Supersymmetric KP Equation

Sasanka GHOSH, Debojit SARMA
Pages: 526 - 538
The N = 2 super-KP equation associated with nonstandard flows is bilinearized using the Hirota method and soliton solutions are obtained. The bilinearization has been done for component fields and its KdV limit is discussed by comparing the soliton solutions obtained by this procedure with those found...

7. A Variational Principle for Volume-Preserving Dynamics

Giuseppe GAETA, Paola MORANDO
Pages: 539 - 554
We provide a variational description of any Liouville, i.e. volume preserving, autnomous vector field on a smooth manifold. This is obtained via a "maximal degree" variational principle; critical sections for this are integral manifolds for the Liouville vector field. We work in coordinates and provide...

8. Toda Equations and -Functions of Genera One and Two

Shigeki MATSUTANI
Pages: 555 - 569
We study the Toda equations in the continuous level, discrete level and ultradiscrete level in terms of elliptic and hyperelliptic and functions of genera one and two. The ultradiscrete Toda equation appears as a discrete-valuation of recursion relations of functions.