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Periodic wave solutions of the Boussinesq equation

Yi Zhang, Ling-ya Ye, Yi-neng Lv and Hai-qiong Zhao

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The Boussinesq equation usually arises in a physical problem as a long wave equation. The present work extends the search of periodic wave solutions for it. The Hirota bilinear method and Riemann theta function are employed in the process. We also analyse the asymptotic property of periodic waves in detail. Furthermore, it is of interest to note that well-known soliton solutions can be reduced from the periodic wave solutions.


PACS

05.45.Yv Solitons

47.35.Fg Solitary waves

MSC

35B10 Periodic solutions

76B25 Solitary waves (See also 35Q51)

35Q51 Solitons (See also 37K40)

Subjects

Fluid dynamics

Statistical physics and nonlinear systems

Dates

Issue 21 (25 May 2007)

Received 16 December 2006, in final form 30 March 2007

Published 8 May 2007



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