| 1. |
- 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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| 2. |
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| 3. |
- 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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| 4. |
- 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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| 5. |
- Euler, Marianna, et al.
(författare)
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On the construction of approximate solutions for a multidimensional nonlinear heat equation
- 1994
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Ingår i: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 27:6, s. 2083-2092
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Tidskriftsartikel (refereegranskat)abstract
- Summary: We study three methods, based on continuous symmetries, to find approximate solutions for the multidimensional nonlinear heat equation $\partial u/\partial x_0+ \Delta u= au^n+ \varepsilon f(u)$, where $a$ and $n$ are arbitrary real constants, $f$ is a smooth function, and $0< \varepsilon\ll 1$.
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| 6. |
- Euler, Marianna, et al.
(författare)
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Symmetries for a class of explicitly space- and time-dependent (1+1)-dimensional wave equations
- 1997
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Ingår i: Proceedings of the second international conference. - Kyev : Institute of Mathematics of the National Academy of Sciences of Ukraine. - 9660203438 ; , s. 70-78
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Konferensbidrag (refereegranskat)abstract
- In this paper the nonlinear wave equation $\partial^2 u/\partial x_0^2-\partial^2 u/\partial x_1^2+f(x_0,x_1,u)=0$, where $f$ is an arbitrary smooth function of its arguments, is considered from the symmetry standpoint. The form of the most general Lie point symmetry generator of this equation is obtained. The classes of functions $f$, for which the equation in question admits a one-parameter Lie point symmetry group, are constructed. Then, the authors investigate the possible form of generators of conformal transformations, assuming the usual form of generators of Lorentz and scaling transformations, and study the wave equations invariant under such operators. The symmetry groups of obtained equations are used for the construction of ansätze and reductions of these equations to ordinary differential equations. $Q$-conditional (nonclassical) symmetries of the wave equation are also considered. Namely, the determining equations for the coefficients of a $Q$-conditional symmetry operator are found and their compatibility is investigated.
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| 7. |
- Euler, Marianna, et al.
(författare)
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Symmetry classification for a coupled nonlinear Schrödinger equation
- 1994
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 1:4, s. 358-379
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Tidskriftsartikel (refereegranskat)abstract
- We do a Lie symmetry classification for a system of two nonlinear coupled Schrödinger equations. Our system under consideration is a generalization of the equations which follow from the analysis of optical fibres. Reductions of some special equations are given.
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| 8. |
- Euler, Norbert
(författare)
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Aktivitet: Journal of Nonlinear Mathematical Physics
- 1997
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Annan publikation (populärvet., debatt m.m.)abstract
- The Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. The latest ISI Impact factor (2005) is: 0.508. Bibliografisk note: http://www.atlantis-press.com/publications/jnmp/
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| 9. |
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| 10. |
- Euler, Norbert, et al.
(författare)
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Conditional and approximate symmetries for a generalized van der Pol equation
- 1994
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Ingår i: Lie Groups and their Applications. ; 1:1, s. 79-94
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Tidskriftsartikel (refereegranskat)abstract
- Non-Lie ansätze and exact solutions are constructed by means of conditional symmetries for a class of nonlinear heat equations in one space dimension. We study approximate symmetries by which one can obtain approximate solutions for multidimensional partial differential equations. The method of approximate symmetries is applied to an $n$-dimensional generalized van der Pol equation. Approximate conditions symmetries are introduced to construct approximate solutions for the latter equation.
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