Elliptical functions and ordinary differential equations

被引：1

作者：

Chouikha, R ^{[1
]}

机构：

[1] UNIV PARIS 13,INST GALILEE,LAB ANAL GEOMETRIE & APPLICAT,UA CNRS 742,F-93430 VILLETANEUSE,FRANCE

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 1997年 / 40卷 / 03期

关键词：

D O I：

10.4153/CMB-1997-034-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we detail some results of a previous note concerning a trigonometric expansion of the Weierstrass elliptic function {p(z); 2omega, 2omega'}. In particular, this implies its classical Fourier expansion. We use a direct integration method of the ODE: (E) is d(2)u/dt(2) = P(u,lambda), u(0) = sigma, du/dt(0) = tau 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.

引用

页码：276 / 284

页数：9