| 1. |
- Euler, Marianna, et al.
(författare)
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Properties of the Calogero-Degasperis-Ibragimov-Shabat differential sequence
- 2011
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Ingår i: Lobachevskii Journal of Mathematics. - 1995-0802 .- 1818-9962. ; 32:1, s. 61-70
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Tidskriftsartikel (refereegranskat)abstract
- We present a differential sequence based upon the Calogero-Degasperis-Ibragimov-Shabat Equation and determine first integrals and the general solution. Under suitable transformations eachmember of the differential sequence can be recast as a product of two factors and we report some of the properties of the factored form.
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| 2. |
- Euler, Marianna, 1961-, et al.
(författare)
-
On Möbius‐invariant and symmetry‐integrable evolution equations and the Schwarzian derivative
- 2019
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Ingår i: Studies in applied mathematics (Cambridge). - : John Wiley & Sons. - 0022-2526 .- 1467-9590. ; 143:2, s. 139-156
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Tidskriftsartikel (refereegranskat)abstract
- We consider symmetry‐integrable evolution equations in 1 + 1 dimensions of order 3 and order 5. We show that there exist only three equations in this class that are invariant under the Möbius transformation, and we name those Schwarzian equations. We report an interesting relation between the recursion operators of the Schwarzian equations and the corresponding adjoint operators that generate hierarchies of Schwarzian systems in terms of the Schwarzian derivative. This indicates a deep relation between the Schwarzian equations and the Schwarzian derivative. A classification of the fully nonlinear third‐order Schwarzian equations is also reported.
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| 3. |
- Euler, Norbert, 1964-, et al.
(författare)
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Local and Nonlocal Symmetries in Mathematical Physics
- 2017
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Taylor & Francis. - 1402-9251 .- 1776-0852. ; 24:Suppl. 1, s. 1-2
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 4. |
- Basarab-Horwath, P., et al.
(författare)
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Amplitude-phase representation for solutions of nonlinear d'Alembert equations
- 1995
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Ingår i: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 28:21, s. 6193-6201
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Tidskriftsartikel (refereegranskat)abstract
- We consider the nonlinear complex d'Alembert equation Square Operator Psi =F( mod Psi mod ) Psi with Psi represented in terms of amplitude and phase, in (1+n)-dimensional Minkowski space. We exploit a compatible d'Alembert-Hamilton system to construct new types of exact solutions for some nonlinearities.
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| 5. |
- Calogero, F., et al.
(författare)
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New evolution PDEs with many isochronous solutions
- 2009
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 353:2, s. 481-488
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Tidskriftsartikel (refereegranskat)abstract
- Certain nonlinear evolution PDEs in 1 + 1 variables (time and space) are identified, featuring a positive parameter ω and evolving, for a large class of initial data, periodically with the fixed period T = 2 π / ω (or perhaps over(T, ̃) = p T with p a small integer). They are autonomous (i.e., they do not feature any explicit dependence on the time variable), but they generally (although not quite all of them) depend explicitly on the space variable hence are not translation-invariant. They are integrable, having been obtained by applying an appropriate change of dependent and independent variables to certain nonlinear evolution PDEs whose integrable character has been recently ascertained. Solutions of some of these PDEs are exhibited.
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| 6. |
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| 7. |
- Duarte, L.G.S., et al.
(författare)
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Invertible point transformations, Painlevé analysis and anharmonic oscillators
- 1990
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Ingår i: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 23, s. 1457-1463
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Tidskriftsartikel (refereegranskat)abstract
- The techniques of an invertible point transformation and the Painleve analysis can be used to construct integrable ordinary differential equations. The authors compare both techniques for anharmonic oscillators.
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| 8. |
- Euler, Marianna, et al.
(författare)
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A class of semilinear fifth-order evolution equations : recursion operators and multipotentialisations
- 2011
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Ingår i: Journal of Nonlinear Mathematical Physics. - 1402-9251 .- 1776-0852. ; 18:Suppl. 1, s. 61-75
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Tidskriftsartikel (refereegranskat)abstract
- We apply a list of criteria which leads to a class of fifth-order symmetry-integrable evolution equations. The recursion operators for this class are given explicitly. Multipotentialisations are then applied to the equations in this class in order to extend this class of integrable equations.
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| 9. |
- Euler, Marianna, 1961-, et al.
(författare)
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Aufgaben, Theorie und Lösungen zur Linearen Algebra, Teil 1 : Der Euklidische Raum
- 2017
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Bok (refereegranskat)abstract
- Dieses Buch ist der erste Teil einer dreiteiligen Serie mit dem Titel Aufgaben, Theorieund L¨osungen zur Linearen Algebra. Dieser erste Teil behandelt Vektoren des euklidischen Raumes sowie Matrizen, Matrixalgebra und Systeme von linearen Gleichungen. Wir l¨osen lineare System mit Hilfe des Gaußschen Eliminationsverfahrens und auf anderem Wege und untersuchen die Eigenschaften dieser Systeme in Bezug auf Vektoren und Matrizen. Dar¨uber hinaus betrachten wir lineare Abbildungen und berechnendie Standardmatrizen dieser Abbildungen.
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| 10. |
- Euler, Marianna, et al.
(författare)
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Explicitly space- and time-dependent d'Alembert equations with symmetries
- 1999
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Ingår i: International Journal of Modern Physics A. - 0217-751X .- 1793-656X. ; 14:26, s. 4189-4200
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Tidskriftsartikel (refereegranskat)abstract
- The general d'Alembert equation $\square u+ f(x_0, x_1,u)= 0$ is considered, where $\square$ is the two-dimensional d'Alembert operator. We classify the equation for functions $f$ by which it admits several Lie symmetry algebras, which include the Lorentz symmetry generator. The corresponding symmetry reductions are listed.
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