Journal of Nonlinear Mathematical Physics

Volume 12, Issue 1, February 2005
Research Article

1. A Chorin-Type Formula for Solutions to a Closure Model for the von K´arm´an­Howarth Equation 1

V.N. Grebenev, M. Oberlack
Pages: 1 - 9
The article is devoted to studying the Millionshtchikov closure model (a particular case of a model introduced by Oberlack [14]) for isotropic turbulence dynamics which appears in the context of the theory of the von K´arm´an-Howarth equation. We write the model in an abstract form that enables us to...
Short Communication

2. A Note on the Degasperis-Procesi Equation

Octavian G. Mustafa
Pages: 10 - 14
We prove that smooth solutions of the Degasperis-Procesi equation have infinite proagation speed: they loose instantly the property of having compact support.
Research Article

3. Generalised Symmetries and the Ermakov-Lewis Invariant

R. Goodall, P.G.L. Leach
Pages: 15 - 26
Generalised symmetries and point symmetries coincide for systems of first-order odinary differential equations and are infinite in number. Systems of linear first-order ordinary differential equations possess a generalised rescaling symmetry. For the sytem of first-order ordinary differential equations...
Short Communication

4. Uniqueness of Steady Symmetric Deep-Water Waves with Vorticity

Pages: 27 - 30
Given a steady and symmetric deep-water wave we prove that the surface profile and the vorticity distribution determine the wave motion completely throughout the fluid.
Research Article

5. Existence of Dual Equations by Means of Strong Necessary Conditions - Analysis of Integrability of Partial Differential Nonlinear Equations

K. Sokalski, T. Wietecha, D. Sokalska
Pages: 31 - 52
A concept of strong necessary conditions for extremum of functional has been aplied for analysis an existence of dual equations for a system of two nonlinear Partial Differential Equations (PDE) in 1+1 dimensions. We consider two types of the dual equations: the Bäcklund transformations and the Bogomolny...
Research Article

6. An L2 Norm Trajectory-Based Local Linearization for Low Order Systems

Fethi Belkhouche
Pages: 53 - 72
This paper presents a linear transformation for low order nonlinear autonomous diferential equations. The procedure consists of a trajectory-based local linearization, which approximates the nonlinear system in the neighborhood of its equilibria. The approximation is possible even in the non-hyperbolic...
Research Article

7. The Structure of Gelfand-Levitan-Marhenko Type Equations for Delsarte Transmutation Operators of Linear Multidimensional Differential Operators and Operator Pencils. Part 1.

Jolanta Golenia, Anatoliy K. Prykarpatsky, Yarema A. Prykarpatsky
Pages: 73 - 87
An analog of Gelfand-Levitan-Marchenko integral equations for multi- dimensional Delsarte transmutation operators is constructed by means of studying their differentiageometric structure based on the classical Lagrange identity for a formally conjugated pair of differential operators. An extension of...
Research Article

8. Solitons and Deformed Lattices I

Betti Hartmann, Wojtek J. Zakrzewski
Pages: 88 - 104
We study a model describing some aspects of the dynamics of biopolymers. The models involve either one or two finite chains with a number N of sites that represent the "units" of a biophysical system. The mechanical degrees of freedom of these chains are coupled to the internal degrees of freedom through...
Research Article

9. A Nonlinearly Dispersive Fifth Order Integrable Equation and its Hierarchy

Ashok Das, Ziemowit Popowicz
Pages: 105 - 117
In this paper, we study the properties of a nonlinearly dispersive integrable system of fifth order and its associated hierarchy. We describe a Lax representation for such a system which leads to two infinite series of conserved charges and two hierarchies of equations that share the same conserved charges....
Research Article

10. q,k-Generalized Gamma and Beta Functions

Rafael Díaz, Carolina Teruel
Pages: 118 - 134
We introduce the q,k-generalized Pochhammer symbol. We construct q,k and Bq,k, the q,k-generalized gamma and beta functions, and show that they satisfy properties that generalize those satisfied by the classical gamma and beta functions. Moreover, we provide integral representations for q,k and Bq,k.
Research Article

11. About the Explicit Characterization of Hamiltonians of the Camassa-Holm Hierarchy

Enrique Loubet
Pages: 135 - 143
We present a detailed computation leading to an explicit formula for the fourth Hamitonian in the series of constants of motion with which any flow of the Camassa-Holm hierarchy is equipped, and explain the inherent difficulties in achieving such explicit expressions for invariants higher in the series.