Journal of Nonlinear Mathematical Physics

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...

We prove that smooth solutions of the Degasperis-Procesi equation have infinite proagation speed: they loose instantly the property of having compact support.

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...

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.

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...

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...

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...

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...

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....

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.

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.