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Mathematical Problems in Engineering
Volume 2009, Article ID 925187, 5 pages
http://dx.doi.org/10.1155/2009/925187
Research Article

Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

1Department of Mathematics, Jiaying University, Meizhou, Guangdong 514015, China
2Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China

Received 4 February 2009; Accepted 7 March 2009

Academic Editor: Ji Huan He

Copyright © 2009 Weimin Zhang. 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. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J.-H. He, “Semi-inverse method of establing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics,” International Journal of Turbo and Jet Engines, vol. 14, no. 1, pp. 23–28, 1997. View at Google Scholar
  3. J.-H. He, “Variational principle for two-dimensional incompressible inviscid flow,” Physics Letters A, vol. 371, no. 1-2, pp. 39–40, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J.-H. He, “Variational approach to (2 + 1)-dimensional dispersive long water equations,” Physics Letters A, vol. 335, no. 2-3, pp. 182–184, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J.-H. He, “A generalized variational principle in micromorphic thermoelasticity,” Mechanics Research Communications, vol. 32, no. 1, pp. 93–98, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J.-H. He, “Variational principle for non-Newtonian lubrication: Rabinowitsch fluid model,” Applied Mathematics and Computation, vol. 157, no. 1, pp. 281–286, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J.-H. He and H.-M. Liu, “Variational approach to diffusion reaction in spherical porous catalyst,” Chemical Engineering and Technology, vol. 27, no. 4, pp. 376–377, 2004. View at Publisher · View at Google Scholar
  8. J.-H. He, H.-M. Liu, and N. Pan, “Variational model for ionomeric polymer-metal composite,” Polymer, vol. 44, no. 26, pp. 8195–8199, 2003. View at Publisher · View at Google Scholar
  9. J.-H. He, “Variational principles for some nonlinear partial differential equations with variable coefficients,” Chaos, Solitons & Fractals, vol. 19, no. 4, pp. 847–851, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-H. He, “A family of variational principles for linear micromorphic elasticity,” Computers & Structures, vol. 81, no. 21, pp. 2079–2085, 2003. View at Google Scholar · View at MathSciNet
  11. H.-M. Liu, “Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method,” Chaos, Solitons & Fractals, vol. 23, no. 2, pp. 573–576, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. Y. Wu, “Variational approach to higher-order water-wave equations,” Chaos, Solitons & Fractals, vol. 32, no. 1, pp. 195–198, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. Wang, Y. Zhou, and Z. Li, “Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics,” Physics Letters A, vol. 216, no. 1–5, pp. 67–75, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. L. Xu, “Variational principles for coupled nonlinear Schrödinger equations,” Physics Letters A, vol. 359, no. 6, pp. 627–629, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  15. 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 Google Scholar
  16. Z.-L. Tao, “Variational principles for some nonlinear wave equations,” Zeitschrift für Naturforschung A, vol. 63, no. 5-6, pp. 237–240, 2008. View at Google Scholar
  17. L. Yao, “Variational theory for the shallow water problem,” Journal of Physics: Conference Series, vol. 96, no. 1, Article ID 012033, 3 pages, 2008. View at Publisher · View at Google Scholar