On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity
In: Journal of Mathematical Physics ; volume 56, issue 2 ; ISSN 0022-2488 1089-7658, 2015
academicJournal
Zugriff:
In this paper, one-dimensional generalized Boussinesq equation: utt − uxx + (u2 + uxx)xx = 0 with boundary conditions ux(0, t) = ux(π, t) = uxxx(0, t) = uxxx(π, t) = 0 is considered. It is proved that the equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with 2-dimensional Diophantine frequencies. The proof is based on an infinite dimensional Kolmogorov-Arnold-Moser theorem and Birkhoff normal form.
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On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity
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Autor/in / Beteiligte Person: | Shi, Yanling ; Xu, Junxiang ; Xu, Xindong ; National Natural Science Foundation of China |
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Zeitschrift: | Journal of Mathematical Physics ; volume 56, issue 2 ; ISSN 0022-2488 1089-7658, 2015 |
Veröffentlichung: | AIP Publishing, 2015 |
Medientyp: | academicJournal |
DOI: | 10.1063/1.4906810 |
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