FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 1, PAGES 207-220

Construction of periodic solutions of a Boussinnesq type equation using the method of quasi-normal forms

A.Yu.Kolesov
N.Kh.Rozov

Using the asymptotic method of quasi-normal forms the dynamic characteristics of the following boundary value problem are analyzed:

$u_{tt}-u_{xx}-\varepsilon a^2 u_{xxtt} = \varepsilon \alpha u_{xxt} + \varepsilon u_t - u^2 u_t,$
$u|_{x=0} = u|_{x=1} = 0, \alpha = const > 0, 0 < \varepsilon << 1. $

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