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- Euler, Norbert, et al.
(author)
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Lie-symmetry vector fields for linear and nonlinear wave equations
- 1989
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In: International journal of theoretical physics. - 0020-7748 .- 1572-9575. ; 28:11, s. 1397-1403
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Journal article (peer-reviewed)abstract
- We derive the Lie symmetry vector fields for the linear wave equation .. u=0 and nonlinear wave equation .. u=u 3. The conformal vector fields for the underlying metric tensor fieldg are also given. We construct the conservation laws and derive similarity solutions. Furthermore, we perform a Painlevé test for the nonlinear wave equation and discuss whether Lie-Bäcklund vector fields exist.
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| 6. |
- Steeb, W-H., et al.
(author)
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Externally driven nonlinear oscillator, Painlevé test, first integrals and Lie symmetries
- 1993
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In: Zeitschrift fur Naturforschung A-A Journal of Physical Sciences. - : Walter de Gruyter GmbH. - 0932-0784 .- 1865-7109. ; 48:8-9, s. 943-944
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Journal article (peer-reviewed)abstract
- Summary: For arbitrary constants $c\sb 1$, $c\sb 2$ and an arbitrary smooth functions $f$ the driven anharmonic oscillator $d\sp 2 u/dt\sp 2+ c\sb 1 du/dt+ c\sb 2 u+u\sp 3= f(t)$ cannot be solved in closed form. We apply the Painlevé test to obtain the constraint on the constants $c\sb 1$, $c\sb 2$ and the function $f$ for which the equation passes the test. We also give the Lie symmetry vector field and first integrals for this equation.
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