| 1. |
- Chanfreau, Philippe, et al.
(författare)
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Viewing the efficiency of chaos control
- 1999
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 6:3, s. 314-331
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Tidskriftsartikel (refereegranskat)abstract
- This paper aims to cast some new light on controlling chaos using the OGY- and the Zero-Spectral-Radius methods. In deriving those methods we use a generalized procedure differing from the usual ones. This procedure allows us to conveniently treat maps to be controlled bringing the orbit to both various saddles and to sources with both real and complex eigenvalues. We demonstrate the procedure and the subsequent control on a variety of maps. We evaluate the control by examining the basins of attraction of the relevant controlled systems graphically and in some cases analytically
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| 2. |
- Euler, Norbert, et al.
(författare)
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Madelung representation for complex nonlinear d'Alembert equations in n-dimensional Minkowski space
- 1995
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 2:3-4, s. 292-300
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Tidskriftsartikel (refereegranskat)abstract
- The Madelung representation $\psi = u\exp(iv)$ is considered for the d'Alembert equation $\square_n\psi - F(|\psi|)\psi = 0$ to develop a technique for finding exact solutions. The authors classify the nonlinear function $F$ for which the amplitude and phase of the d'Alembert equation are related to the solutions of the compatible d'Alembert-Hamiltonian system. The equations are studied in the $n$-dimensional Minkowski space.[A.~Ju.~Obolenskij (Kyïv)]
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| 3. |
- Euler, Norbert
(författare)
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Transformation properties of x''+f1(t)x + f2(t)x + f3(t)xn = 0
- 1997
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 4:3-4, s. 310-337
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Tidskriftsartikel (refereegranskat)abstract
- The author studies the integrability of the nonlinear second-order ordinary differential equation described in the title. Using the invertible point transformation technique, Lie point symmetry technique and the Painlevé analysis, he classifies all integrable cases. The Lie algebra structure of the Lie point symmetries is also discussed. Finally, the three different methods are compared.
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| 4. |
- Wall, Peter
(författare)
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Some homogenization and corrector results for nonlinear monotone operators
- 1998
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 5:2, s. 331-348
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form - div (a (x, x/h, Duh)) = fh on with Dirichlet boundary conditions. The sequence (h) tends to 0 and the map a(x, y, ) is periodic in y, monotone in and satisfies suitable continuity conditions. It is proved that uh u weakly in H1,2 0 (), where u is the solution of a homogenized problem - div(b(x, Du)) = f on . We also prove some corrector results, i.e. we find (Ph) such that Duh - Ph(Du) 0 in L2 (, Rn ).
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| 5. |
- Kotov, A
(författare)
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Poisson homology of r-matrix type orbits I: Example of computation
- 1999
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Ingår i: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS. - : NORBERT EULER. - 1402-9251. ; 6:4, s. 365-383
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the Poisson algebraic structure associated with a classical r-matrix, i.e. with a solution of the modified classical Yang-Baxter equation. In Section 1 we recall the concept and basic facts of the r-matrix type Poisson orbits. Th
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