On the integrability of double cosine and sine series, II
✍ Scribed by Ferenc Móricz
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 589 KB
- Volume
- 154
- Category
- Article
- ISSN
- 0022-247X
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📜 SIMILAR VOLUMES
In this paper we study weighted integrability of the sum of double cosine series. w The results obtained extend a theorem of Moricz Proc. Amer. Math. Soc. 109 ## Ž . x p 1990 417᎐425 on L -integrability of double cosine series and two theorems of w Ž . x p
We discuss the numerical computation of the cosine lemniscate function and its inverse, the lemniscate integral. These were previously studied by Bernoulli, Euler, Gauss, Abel, Jacobi and Ramanujan. We review general elliptic formulas for this special case and provide some novelties. We show that a
completely integrable through the inverse scattering transform (see, for example, [1,11]) this allows us to study the In this, the first of two papers on the numerical solution of the sine-Gordon equation, we investigate the numerical behavior of a subsequent nonlinear evolution of the instabilities