Journal of Nonlinear Mathematical Physics

Volume 15, Issue 2, August 2008

1. Cocycles and stream functions in quasigeostrophic motion

Cornelia Vizman
Pages: 140 - 146
We present a geometric version of the Lie algebra 2-cocycle connected to quasi- geostrophic motion in the beta-plane approximation. We write down an Euler equation for the fluid velocity, corresponding to the evolution equation for the stream function in quasigeostrophic motion.

2. Fourth-order recursion operators for third-order evolution equations

Marianna Euler
Pages: 147 - 151
We report the recursion operators for a class of symmetry integrable evolution equations of third order which admit fourth-order recursion operators. Under the given assumptions we obtain the complete list of equations, one of which is the well-known Krichever-Novikov equation.

3. Lagrangian formulation of a generalized Lane-Emden equation and double reduction

C. Masood KHALIQUE, Fazal M. MAHOMED, Ben MUATJETJEJA
Pages: 152 - 161
We classify the Noether point symmetries of a generalized Lane-Emden equation. We obtain first integrals of the various cases which admit Noether point symmetry and find reduction to quadratures for these cases. Three new cases are found for the function f (y). One of them is f (y) = ?y r, where r

4. On the propagation of vector ultra-short pulses

Monika PIETRZYK, I. KANATTSIKOV, Uwe BANDELOW
Pages: 162 - 170
A two component vector generalization of the Sch ?afer-Wayne short pulse equation is derived. It describes propagation of ultra-short pulses in optical fibers with Kerr nonlinearity beyond the slowly varying envelope approximation and takes into account the effects of anisotropy and polarization. We...

5. On bi-hamiltonian structure of some integrable systems

A.V. TSIGANOV
Pages: 171 - 185
We classify quadratic Poisson structures on so (4) and e(3), which have the same foliations by symplectic leaves as canonical Lie-Poisson tensors. The separated variables for some of the corresponding bi-integrable systems are constructed.

6. Solitary waves in helicoidal models of DNA dynamics

Giuseppe GAETA, Laura VENIER
Pages: 186 - 204
We analyze travelling solitary wave solutions in the Barbi-Cocco-Peyrard and in a simplified version of the Cocco-Monasson models of nonlinear DNA dynamics. We identify conditions to be satisfied by parameters for such solutions to exist, and provide first order ODEs whose solutions give the required...

7. Lie symmetries of a Painleve-type equation without Lie symmetries

M.C. NUCCI
Pages: 205 - 211
We use a method inspired by the Jacobi last multiplier [M.C. Nucci, Jacobi last multiplier and Lie symmetries: a novel application of an old relationship, J. Nonlinear Math. Phys. 12, 284-304 (2005)] in order to find Lie symmetries of a Painlev ?e-type equation without Lie point symmetries.

8. On a classification of integrable vectorial evolutionary equations

M. Ju Balakhnev, A.G. Meshkov
Pages: 212 - 226
A list of twenty five integrable vectorial evolutionary equations of the third order is presented. Each equation from the list possesses higher symmerties and higher conservation laws.

9. Lie algebra methods for the applications to the statistical theory of turbulence

V.N. GREBENEV, M. OBERLACK, A.N. GRISHKOV
Pages: 227 - 251
Approximate Lie symmetries of the Navier-Stokes equations are used for the applica- tions to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to...

10. Decomposition of symmetric tensor fields in the presence of a flat contact pro jective structure

Yael FREGIER, Pierre MATHONET, Norbert PONCIN
Pages: 252 - 269
Let M be an odd-dimensional Euclidean space endowed with a contact 1-form ?. We investigate the space of symmetric contravariant tensor fields over M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up of those vector fields that preserve the contact structure...