Pages: 1 - 9
The article is devoted to studying the Millionshtchikov closure model (a particular
case of a model introduced by Oberlack ) 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...
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.
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...
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.
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...
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...
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...
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...
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...
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.
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.