Journal of Nonlinear Mathematical Physics

Volume 9, Issue 1, February 2002
Research Article

1. Kovalevski Exponents and Integrability Properties in Class A Homogeneous Cosmological Models

Marek Szydłowski, Marek Biesiada
Pages: 1 - 10
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 class...
Research Article

2. The Matrix Kadomtsev­Petviashvili Equation as a Source of Integrable Nonlinear Equations

Attilio Maccari
Pages: 11 - 20
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....
Research Article

3. On Integrability of Differential Constraints Arising from the Singularity Analysis

S. Yu. Sakovich
Pages: 21 - 25
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...
Research Article

4. Hierarchy of Chaotic Maps with an Invariant Measure and their Compositions

M.A. Jafarizadeh, S. Behnia
Pages: 26 - 41
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...
Research Article

5. On Weak Convergence of Locally Periodic Functions

Dag Lukkassen, Peter Wall
Pages: 42 - 57
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.
Research Article

6. Soliton Asymptotics of Rear Part of Non-Localized Solutions of the Kadomtsev-Petviashvili Equation

Anne Boutet de Monvel, Eugene Khruslov
Pages: 58 - 76
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.
Research Article

7. The Numerical Study of the Solution of the 4 0 Model

S. Gladkoff, A. Alaie, Y. Sansonnet, M. Manolessou
Pages: 77 - 85
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...
Research Article

8. Distinguishing Three-Dimensional Lens Spaces L(7, 1) and L(7, 2) by Means of Classical Pentagon Equation

I.G. Korepanov, E.V. Martyushev
Pages: 86 - 98
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...
Research Article

9. Periodic Motions Galore: How to Modify Nonlinear Evolution Equations so that They Feature a Lot of Periodic Solutions

F. Calogero, J-P Françoise
Pages: 99 - 125
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.