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| 2. |
- Duarte, L.G.S., et al.
(author)
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Invertible point transformations, Painlevé analysis and anharmonic oscillators
- 1990
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In: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 23, s. 1457-1463
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Journal article (peer-reviewed)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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| 3. |
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| 4. |
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| 5. |
- Euler, Norbert, et al.
(author)
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Invertible point transformations, Painlevé test, and the second Painlevé transcendent
- 1991
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In: International journal of theoretical physics. - 0020-7748 .- 1572-9575. ; 30:9, s. 1267-1271
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Journal article (peer-reviewed)abstract
- The techniques of invertible point transformations and the Painlevé analysis can be used to construct integrable ordinary differential equations. We compare both techniques for the second Painlevé transcendent.
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| 6. |
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| 7. |
- Euler, Norbert, et al.
(author)
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Lie symmetries and Painlevé test for explicitly space- and time-dependent nonlinear wave equations
- 1993
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In: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 26, s. 307-313
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Journal article (peer-reviewed)abstract
- The authors investigate the Lie symmetry vector fields of the wave equation Square Operator u+f(x1, . . ., xn, u)=0 where f is some nonlinear smooth function and n>or=2. The Painleve test is considered for the construction of explicitly space- and time-dependent integrable one-space-dimensional nonlinear wave equations.
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| 8. |
- Euler, Norbert, et al.
(author)
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On exact solutions for damped anharmonic oscillators
- 1989
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In: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 22, s. 195-199
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Journal article (peer-reviewed)abstract
- For arbitrary functions f1, f2 and f3 the anharmonic oscillator x+f1(t)x+f2(t)x+f3(t)x3=0 cannot be solved in closed form (i.e. the general solution cannot be expressed as elliptic functions). The authors apply the Painleve test to obtain the constraint on the functions f1, f2 and f3 for which the equation passes the test. The constraint on f1, f2 and f3 (i.e the differential equation which f1, f2, and f3 obey) is discussed and solutions are given.
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| 9. |
- Euler, Norbert, et al.
(author)
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Polynomial field theories and nonintegrability
- 1990
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In: Physica Scripta. - : IOP Publishing. - 0031-8949 .- 1402-4896. ; 41, s. 289-291
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Journal article (peer-reviewed)abstract
- The nonintegrability of the nonlinear field equation vrli = v3 is studied with the help of the Painlev6 test. The condition at the resonance is discussed in detail. Particluar solutions are given.
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| 10. |
- Euler, Norbert, et al.
(author)
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Symmetries of a nonlinear equation in plasma physics
- 1991
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In: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 24:14, s. 785-787
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Journal article (peer-reviewed)abstract
- The Lie symmetry vector fields are derived for a nonlinear equation in plasma physics.
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