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Mathematical Problems in Engineering
Volume 2009, Article ID 509390, 10 pages
http://dx.doi.org/10.1155/2009/509390
Research Article

Soliton and Periodic Wave Solutions to the Osmosis Equation

Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 7 May 2009; Accepted 9 July 2009

Academic Editor: Shijun Liao

Copyright © 2009 Jiangbo Zhou 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.

Linked References

  1. P. Rosenau and J. M. Hyman, “Compactons: solitons with finite wavelength,” Physical Review Letters, vol. 70, no. 5, pp. 564–567, 1993. View at Publisher · View at Google Scholar
  2. A. M. Wazwaz, “Compactons and solitary patterns structures for variants of the KdV and the KP equations,” Applied Mathematics and Computation, vol. 139, no. 1, pp. 37–54, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J.-H. He, “Homotopy perturbation method for bifurcation of nonlinear problems,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 6, no. 2, pp. 207–208, 2005. View at Google Scholar
  4. J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700–708, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J.-H. He and X.-H. Wu, “Construction of solitary solution and compacton-like solution by variational iteration method,” Chaos, Solitons & Fractals, vol. 29, no. 1, pp. 108–113, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. L. Xu, “Variational approach to solitons of nonlinear dispersive K(m,n) equations,” Chaos, Solitons & Fractals, vol. 37, no. 1, pp. 137–143, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. M. Wazwaz, “General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations mK(n,n) in higher dimensional spaces,” Mathematics and Computers in Simulation, vol. 59, no. 6, pp. 519–531, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. M. Wazwaz, “Compact and noncompact structures for a variant of KdV equation in higher dimensions,” Applied Mathematics and Computation, vol. 132, no. 1, pp. 29–45, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Y. Chen, B. Li, and H. Q. Zhang, “New exact solutions for modified nonlinear dispersive equations mK(m,n) in higher dimensions spaces,” Mathematics and Computers in Simulation, vol. 64, no. 5, pp. 549–559, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. B. He, Q. Meng, W. Rui, and Y. Long, “Bifurcations of travelling wave solutions for the mK(n,n) equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 10, pp. 2114–2123, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Z. Y. Yan, “Modified nonlinearly dispersive mK(m,n,k) equations. I. New compacton solutions and solitary pattern solutions,” Computer Physics Communications, vol. 152, no. 1, pp. 25–33, 2003. View at Google Scholar · View at MathSciNet
  13. Z. Y. Yan, “Modified nonlinearly dispersive mK(m,n,k) equations. II. Jacobi elliptic function solutions,” Computer Physics Communications, vol. 153, no. 1, pp. 1–16, 2003. View at Google Scholar · View at MathSciNet
  14. A. Biswas, “1-soliton solution of the K(m,n) equation with generalized evolution,” Physics Letters A, vol. 372, no. 25, pp. 4601–4602, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  15. Y. G. Zhu, K. Tong, and T. C. Lu, “New exact solitary-wave solutions for the K(2,2,1) and K(3,3,1) equations,” Chaos, Solitons & Fractals, vol. 33, no. 4, pp. 1411–1416, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. C. Xu and L. Tian, “The bifurcation and peakon for K(2,2) equation with osmosis dispersion,” Chaos, Solitons & Fractals, vol. 40, no. 2, pp. 893–901, 2009. View at Publisher · View at Google Scholar
  17. J. Zhou and L. Tian, “Soliton solution of the osmosis K(2,2) equation,” Physics Letters A, vol. 372, no. 41, pp. 6232–6234, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  18. V. O. Vakhnenko and E. J. Parkes, “Explicit solutions of the Camassa-Holm equation,” Chaos, Solitons & Fractals, vol. 26, no. 5, pp. 1309–1316, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. V. O. Vakhnenko and E. J. Parkes, “Periodic and solitary-wave solutions of the Degasperis-Procesi equation,” Chaos, Solitons & Fractals, vol. 20, no. 5, pp. 1059–1073, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. E. J. Parkes, “The stability of solutions of Vakhnenko's equation,” Journal of Physics A, vol. 26, no. 22, pp. 6469–6475, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Scientists, Die Grundlehren der Mathematischen Wissenschaften, vol. 67, Springer, Berlin, Germany, 2nd edition, 1971. View at MathSciNet
  22. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1972.