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ISSN 1088-6850(e) ISSN 0002-9947(p)

A hypergeometric function approach to the persistence problem of single sine-Gordon breathers

Author(s): Jochen Denzler
Journal: Trans. Amer. Math. Soc. 349 (1997), 4053-4083.
MSC (1991): Primary 35Q53; Secondary 33C05, 35B10, 44A10
MathSciNet review: 1422601
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Abstract: It is shown that for an interesting class of perturbation functions, at most one of the continuum of sine-Gordon breathers can persist for the perturbed equation. This question is much more subtle than the question of persistence of large portions of the family, because analytic continuation arguments in the amplitude parameter are no longer available. Instead, an asymptotic analysis of the obstructions to persistence for large Fourier orders is made, and it is connected to the asymptotic behaviour of the Taylor coefficients of the perturbation function by means of an inverse Laplace transform and an integral transform whose kernel involves hypergeometric functions in a way that is degenerate in that asymptotic analysis involves a splitting monkey saddle. Only first order perturbation theory enters into the argument. The reasoning can in principle be carried over to other perturbation functions than the ones considered here.

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For the readers' convenience: the above are referred to in the following sections: [1]: 5.1.2, 5.1.3, 5.2.2, 5.2.4 - [2]: 1, 2, 3.1, 6.3 - [3]: 5.1.3 - [4]: 5.2.1, 5.2.2 - [5]: 5.1.3 - [6]: 3.3 - [7]: 1, 2, 3.1, 6.3 - [8]: 3.1, 6.3 - [10]: 5.1.3 - [11]: 6.1 - [12],[13]: 6.3 - [14],[15]: 5.1.3 - [16]: 6.3 - [18],[19]: 6.3 - [9],[17]: general ref. for Laplace transform

As the items [12] and [19] may be difficult to obtain in many libraries, some readers may find the e-mail addresses of the respective authors useful, namely: bgonzalez@ull.es, enegrin@ull.es, nhayek@ull.es and semen@mmf.bsu.minsk.by respectively. The e-mail address of the Revista Técnica is retecin@luz.ve. They are also availabe from Math. Reviews through the MathDoc service.

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