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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 309420, 4 pages
Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation
Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
Received 22 January 2014; Accepted 21 February 2014; Published 27 March 2014
Academic Editor: Baojian Hong
Copyright © 2014 Dianchen Lu and Jie Liu. 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.
- J. H. He, “A simple perturbation approach to Blasius equation,” Applied Mathematics and Computation, vol. 140, no. 2-3, pp. 217–222, 2003.
- J. H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 695–700, 2005.
- 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.
- H. S. Fu, L. Cao, and B. Han, “A homotopy perturbation method for well log constrained seismic waveform inversion,” Chinese Journal of Geophysics, vol. 55, no. 9, pp. 2173–2179, 2004.
- L. F. Shi and X. C. Zhou, “Homotopic mapping solution of soliton for a class of disturbed Burgers equation,” Acta Physica Sinica, vol. 59, no. 5, pp. 2915–2918, 2010.
- D. D. Ganji and A. Sadighi, “Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 4, pp. 411–418, 2006.
- M. Gorji, D. D. Ganji, and S. Soleimani, “New application of He's homotopy perturbation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 3, pp. 319–328, 2007.
- Y. R. Shi, X. J. Xu, Z. X. Wu et al., “Application of the homotopy analysis method to solving nonlinear evolution equations,” Acta Physica Sinica, vol. 55, no. 4, pp. 1555–1560, 2006.
- J. Q. Mo and J. S. Yao, “Homotopic mapping method for the solution of soliton to a perturbed KdV equation,” Acta Physica Sinica, vol. 57, no. 12, pp. 7419–7422, 2008.
- L. F. Shi and J. Q. Mo, “Soliton-like homotopic approximate analytic solution for a disturbed nonlinear evolution equation,” Acta Physica Sinica, vol. 58, no. 12, pp. 8123–8126, 2009.
- S. Liao, “Comparison between the homotopy analysis method and homotopy perturbation method,” Applied Mathematics and Computation, vol. 169, no. 2, pp. 1186–1194, 2005.
- Y. R. Shi and H. J. Yang, “Application of a homotopy analysis method to solving a dissipative system,” Acta Physica Sinica, vol. 59, no. 1, pp. 67–74, 2010.
- J. H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters A, vol. 350, no. 1-2, pp. 87–88, 2006.
- G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988.
- G. Adomian, Nonlinear Stochastic Systems and Applications to Physics, Kluwer Academic Publishers Group, Dordrecht, The Netherlands, 1989.
- S. Abbasbandy, “A numerical solution of Blasius equation by Adomian's decomposition method and comparison with homotopy perturbation method,” Chaos, Solitons and Fractals, vol. 31, no. 1, pp. 257–260, 2007.
- S. Abbasbandy and M. T. Darvishi, “A numerical solution of Burgers' equation by modified Adomian method,” Applied Mathematics and Computation, vol. 163, no. 3, pp. 1265–1272, 2005.
- M. A. Malkov, “Spatial chaos in weakly dispersive and viscous media: a nonperturbative theory of the driven KdV-Burgers equation,” Physica D: Nonlinear Phenomena, vol. 95, no. 1, pp. 62–80, 1996.
- K. Y. Guan and G. Gao, “Qualitative analysis and traveling wave solutions of the Burgers-KdV equation,” Science in China A, vol. 30, no. 1, pp. 64–73, 1987.
- S. D. Liu and S. S. Liu, “KdV-Burgers equation modelling of turbulence,” Science in China A, vol. 34, no. 9, pp. 938–945, 1991.
- B. Hong, “New Jacobi elliptic functions solutions for the variable-coefficient MKdV equation,” Applied Mathematics and Computation, vol. 215, no. 8, pp. 2908–2913, 2009.
- S. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Press, New York, NY, USA, 2004.