Skip to main content

News about Scitation

In December 2016 Scitation will launch with a new design, enhanced navigation and a much improved user experience.

To ensure a smooth transition, from today, we are temporarily stopping new account registration and single article purchases. If you already have an account you can continue to use the site as normal.

For help or more information please visit our FAQs.

banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
1. L. Wei and Y. He, “Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional KdV-Burgers-Kuramoto equation,” Cornell University Library. arXiv:1201.1156v1 (2012).
2. T. Kawahara, “Formation of saturated solitons in a nonlinear dispersive system with instability and dissipation,” Phys. Rev. Lett. 51, 381383 (1983).
3. J. Topper and T. Kawahara, “Approximate equations for long nonlinear waves on a viscous fluid,” J. Physical Society of Japan 44, 663666 (1978).
4. B. Cohen, J. Krommes, W. Tang, and M. Rosenbluth, “Non-linear saturation of the dissipative trapped-ion mode by mode coupling,” Nuclear Fusion 16, 971992 (1976).
5. F. Huang and S. Liu, “Physical mechanism and model of turbulent cascades in a barotropic atmosphere,” Adv. Atmos. Sci. 21, 3440 (2004).
6. L. Song and H. Zhang, “Application of homotopy analysis method to fractional KdV–Burgers–Kuramoto equation,” Physics Letter A 367, 8894 (2007).
7. M. Safari, D. D. Ganji, and M. Moslemi, “Application of He's variational iteration method and Adomian's decomposition method to the fractional KdV–Burgers–Kuramoto equation,” Computers and Mathematics with Applications, 58, 20912097 (2009).
8. I. Podlubny, Fractional Differential Equations (Academic Press, New York, 1999).
9. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and derivatives: Theory and Applications (Taylor and Francis, London, 1993).
10. M. Razzaghi and S. Yousefi, “The Legendre wavelets operational matrix of integration,” Int. J. Syst. Sci. 32, 495502 (2001).
11. M. Rehman and R. A. Khan, “The Legendre wavelet method for solving fractional differential equations,” Commun Nonlinear Sci Numer Simulat 16, 41634173 (2011).
12. L. Nanshan and E. B. Lin, “Legendre wavelet method for numerical solutions of partial differential equations,” Numer. Methods Partial Differ. Equ. 26(1), 8194 (2010).

Data & Media loading...


Article metrics loading...



In this paper, KdV-Burger-Kuramoto equation involving instability, dissipation, and dispersion parameters is solved numerically. The numerical solution for the fractional order KdV-Burger-Kuramoto (KBK) equation has been presented using two-dimensional Legendre wavelet method. The approximate solutions of nonlinear fractional KBK equation thus obtained by Legendre wavelet method are compared with the exact solutions. The present scheme is very simple, effective and convenient for obtaining numerical solution of the KBK equation.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd