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.
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
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
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....
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.
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...
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.
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.
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...
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...