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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 185469, 11 pages
Exact Periodic Solutions of the Nonintegrable Kawahara Equation
Department of Applied Mathematics and Informatics, Technical University of Sofia, P.O. Box 384,
1000 Sofia, Bulgaria
Received 26 April 2012; Accepted 19 July 2012
Academic Editors: M. Ehrnström, K. S. Fa, D. Gepner, and W.-H. Steeb
Copyright © 2012 Ognyan Yordanov Kamenov and Anna P. Angova. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- T. Kawahara, “Oscillatory solitary waves in dispersive media,” Journal of the Physical Society of Japan, vol. 33, no. 1, pp. 260–264, 1972.
- Y. Yamamoto, “Head-on collision of shallow-water solitary waves near the critical depth where dispersion due to gravity balances with that due to surface tension,” Journal of the Physical Society of Japan, vol. 58, no. 12, pp. 4410–4415, 1989.
- M. Ablowtz and H. Segur, Solitons and the Inverse Scattering Transform, Cambridge University Press, New York, NY, USA, 2006.
- K. Kano and T. Nakayama, “An exact solution of the wave equation: ,” Journal of the Physical Society of Japan, vol. 50, no. 2, pp. 361–362, 1981.
- Y. Yamamoto and E. Takizawa, “On a solution on non-linear time-evolution equation of fifth order,” Journal of the Physical Society of Japan, vol. 50, no. 5, pp. 1421–1422, 1981.
- J. P. Boyd, “Solitons from sine waves: analytical and numerical methods for non-integrable solitary and cnoidal waves,” Physica D, vol. 21, no. 2-3, pp. 227–246, 1986.
- J. K. Hunter and J. Scheurle, “Existence of perturbed solitary wave solutions to a model equation for water waves,” Physica D, vol. 32, no. 2, pp. 253–268, 1988.
- N. G. Berloff and L. N. Howard, “Solitary and periodic solutions of nonlinear nonintegrable equations,” Studies in Applied Mathematics, vol. 99, no. 1, pp. 1–24, 1997.
- M. Weiss, M. Tabor, and G. Carneval, “The Painleve property for partial differential equation,” Journal of Mathematical Physics, vol. 24, no. 3, pp. 522–526, 1983.
- O. Y. Kamenov, “Exact periodic solutions of the sixth-order generalized Boussinesq equation,” Journal of Physics A, vol. 42, no. 37, Article ID 375501, 11 pages, 2009.
- R. Hirota, “Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices,” Journal of Mathematical Physics, vol. 14, no. 7, pp. 810–814, 1973.
- Y. Matsuno, Bilinear Transformation Method, Academic Press, New York, NY, USA, 1984.
- R. Hirota and J. Satsumai, “N-soliton solutions of model equations for shallow water waves,” Journal of the Physical Society of Japan, vol. 40, no. 2, pp. 611–612, 1976.
- E. Janke, F. Emde, and F. Lösch, Tafeln Höherer Funktionen, B.G. Teubner, Stuttgart, Germany, 1960.
- M. Toda, Theory of Nonlinear Lattices, Springer, New York, NY, USA, 1979.