Qualitative approach to homogeneous anisotropic Bianchi class A models in terms
of dynamical systems reveals a hierarchy of invariant manifolds. By calculating the
Kovalevski Exponents according to Adler - van Moerbecke method we discuss how
algebraic integrability property is distributed in this...
A new integrable class of DaveyStewartson type systems of nonlinear partial diffrential equations (NPDEs) in 2+1 dimensions is derived from the matrix Kadomtsev
Petviashvili equation by means of an asymptotically exact nonlinear reduction method
based on Fourier expansion and spatio-temporal rescaling....
Integrability of differential constraints arising from the singularity analysis of two
(1+1)-dimensional second-order evolution equations is studied. Two nonlinear ordnary differential equations are obtained in this way, which are integrable by quadrtures in spite of very complicated branching of their...
We give a hierarchy of many-parameter families of maps of the interval [0, 1] with an
invariant measure and using the measure, we calculate KolmogorovSinai entropy of
these maps analytically. In contrary to the usual one-dimensional maps these maps
do not possess period doubling or period-n-tupling...
We prove a generalization of the fact that periodic functions converge weakly to the
mean value as the oscillation increases. Some convergence questions connected to
locally periodic nonlinear boandary value problems are also considered.
We construct non-localized, real global solutions of the Kadomtsev-Petviashvili-I eqution which vanish for x - and study their large time asymptotic behavior. We
prove that such solutions eject (for t ) a train of curved asymptotic solitons which
move behind the basic wave packet.
We present a numerical study of the nonlinear system of 4
0 equations of motion.
The solution is obtained iteratively, starting from a precise point-sequence of the
appropriate Banach space, for small values of the coupling constant. The numerical
results are in perfect agreement with the main theoretical...
We construct new topological invariants of three-dimensional manifolds which can,
in particular, distinguish homotopy equivalent lens spaces L(7, 1) and L(7, 2). The
invariants are built on the base of a classical (not quantum) solution of pentagon
equation, i.e. algebraic relation corresponding to...
A simple trick is illustrated, whereby nonlinear evolution equations can be modified so
that they feature a lot or, in some cases, only periodic solutions. Several examples
(ODEs and PDEs) are exhibited.