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Fonctions elliptiques et équations différentielles ordinaires

  Published:1997-09-01
 Printed: Sep 1997
  • Raouf Chouikha
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Abstract

In this paper, we detail some results of a previous note concerning a trigonometric expansion of the Weierstrass elliptic function $\{\wp(z);\, 2\omega, 2\omega'\}$. In particular, this implies its classical Fourier expansion. We use a direct integration method of the ODE $$(E)\left\{\matrix{{d^2u \over dt^2} = P(u, \lambda)\hfill \cr u(0) = \sigma\hfill \cr {du \over dt}(0) = \tau\hfill \cr}\right.$$ where $P(u)$ is a polynomial of degree $n = 2$ or $3$. In this case, the bifurcations of $(E)$ depend on one parameter only. Moreover, this global method seems not to apply to the cases $n > 3$.
MSC Classifications: 33E05, 34A05, 33E20, 33E30, 34A20, 34C23 show english descriptions Elliptic functions and integrals
Explicit solutions and reductions
Other functions defined by series and integrals
Other functions coming from differential, difference and integral equations
unknown classification 34A20
Bifurcation [See also 37Gxx]
33E05 - Elliptic functions and integrals
34A05 - Explicit solutions and reductions
33E20 - Other functions defined by series and integrals
33E30 - Other functions coming from differential, difference and integral equations
34A20 - unknown classification 34A20
34C23 - Bifurcation [See also 37Gxx]
 

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