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ISRN Mathematical Physics
Volume 2013 (2013), Article ID 673546, 8 pages
The Coupled Kuramoto-Sivashinsky-KdV Equations for Surface Wave in Multilayered Liquid Films
1Department of Mathematics, Weber State University, Ogden, UT 84408, USA
2Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA
3Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
Received 4 June 2013; Accepted 5 July 2013
Academic Editors: S. C. Lim and W.-H. Steeb
Copyright © 2013 Maomao Cai et al. 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.
- B. A. Malomed, B. F. Feng, and T. Kawahara, “Stabilized Kuramoto-Sivashinsky system,” Physical Review E, vol. 64, no. 4, Article ID 046304, 9 pages, 2001.
- B. F. Feng, B. A. Malomed, and T. Kawahara, “Cylindrical solitary pulses in a two-dimensional stabilized Kuramoto-Sivashinsky system,” Physica D, vol. 175, no. 3-4, pp. 127–138, 2003.
- D. J. Benney, “Long waves on liquid films,” Journal of Mathematical Physics, vol. 45, pp. 150–155, 1966.
- C. I. Christov and M. G. Velarde, “Dissipative solitons,” Physica D, vol. 86, no. 1-2, pp. 323–347, 1995.
- C. Elphick, G. R. Ierley, O. Regev, and E. A. Spiegel, “Interacting localized structures with Galilean invariance,” Physical Review A, vol. 44, no. 2, pp. 1110–1122, 1991.
- J. A. Gear and R. Grimshaw, “Weak and strong interactions between internal solitary waves,” Studies in Applied Mathematics, vol. 70, no. 3, pp. 235–258, 1984.
- Y. Lenbury, D. Li, and C. Rattanakul, “Stability of solution of Kuramoto-Sivashinsky-Korteweg-de Vries system,” Computers & Mathematics with Applications, vol. 52, no. 3-4, pp. 497–508, 2006.
- X. Carvajal and M. Panthee, “Sharp local well-posedness of KdV type equations with dissipative perturbations,” http://arxiv.org/abs/1304.6640.
- M. Cai and D. Li, “Global solutions for coupled Kuramoto-Sivashinsky-KdV system,” Quarterly of Applied Mathematics, vol. 67, no. 3, pp. 477–488, 2009.
- M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations, vol. 13 of Texts in Applied Mathematics, Springer, New York, NY, USA, 2004.
- B. F. Feng, B. A. Malomed, and T. Kawahara, “Stable periodic waves in coupled Kuramoto-Sivashinsky-Korteweg-de Vries equations,” Journal of the Physical Society of Japan, vol. 71, no. 11, pp. 2700–2707, 2002.
- O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, vol. 49 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1985.
- T. Kato, “The Cauchy problem for quasi-linear symmetric hyperbolic systems,” Archive for Rational Mechanics and Analysis, vol. 58, no. 3, pp. 181–205, 1975.