References

ANALYTICAL SOLUTION OF REGULARIZED LONG WAVE (RLW) EQUATION WITH HOMOTOPY ANALYSIS METHOD


[1] S. Abbasbandy, The application of homotopy analysis method to nonlinear equations arising in heat transfer, Phys. Lett. A 360 (2006), 109-113.

[2] G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl. 135 (1988), 501-544.

[3] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, MA, 1994.

[4] J. L. Bona, W. G. Pritchard and L. R. Scott, Numerical scheme for a model of nonlinear dispersive waves, J. Comput. Phys. 60 (1985), 167-176.

[5] I. Dag, Application of cubic B-splines for numerical solution of the RLW equation, Appl. Math. Comput. 159 (2004), 373-389.

[6] G. Eilenberger, Solitons, Mathematical Methods for Physicists, Springer-Verlag, 1983.

[7] T. S. El-Danaf, M. A. Ramadan and F. E. I. Abd Alaal, The use of Adomian decomposition method for solving the regularized long-wave equation, Chaos, Solitons and Fractals 26 (2005), 747-757.

[8] A. Esen and S. Kutluay, Application of a lumped Galerkin method to the regularized long wave equation, Appl. Math. Comput. 174 (2006), 833-845.

[9] E. Fan, Two new applications of the homogeneous balance method, Physics Letters A 256 (2000), 353-357.

[10] P. Gray and S. Scott, Chemical Oscillations and Instabilities, Clarendon, Oxford, 1990.

[11] A. Hasegawa, Plasma Instabilities and Nonlinear Effects, Springer-Verlag, Berlin, 1975.

[12] T. Hayat, M. Khan and S. Asghar, Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid, Acta Mech. 168 (2004), 213-232.

[13] J. H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput. 114 (2000), 115-123.

[14] J. H. He, Comparison of homotopy perturbation and homotopy analysis method, Appl. Math. Comput. (2004), 156-527.

[15] J. H. He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. 20 (2006), 1141-1199.

[16] X. B. Hu and Y. T. Wu, Application of the Hirota bilinear formalism to a new integrable-difference equation, Physics Letters A 246 (1998).

[17] S. J. Liao, On the Proposed Homotopy Analysis Technique for Nonlinear Problems and its Applications, Ph.D. Dissertation, Shanghai Jio Tong University, 1992.

[18] S. J. Liao, Numerically solving nonlinear problems by the homotopy analysis method, Comput. Mech. 20 (1997), 530-540.

[19] S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Press, Chapman and Hall, Boca Raton 17 (2003), 1-16.

[20] D. H. Pregrine, Calculations of the development of an undular bore, J. Fluid Mech. 25 (1996), 321-330.

[21] K. R. Raslan, A computational method for the regularized long wave equation, Appl. Math. Comput. 167 (2005), 1101-1118.

[22] S. Sasha Ray, A numerical solution of coupled sine-Gordon equation by using the modified decomposition method, Appl. Math. Comput. 175 (2006).

[23] M. Sajid, T. Hayat and S. Asghar, Comparison between HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt, Nonlinear Dyn. 50 (2007), 27-35.

[24] S. I. Saki, Solitary waves of RLW equation, Comput. Phys. Commun. 138 (2001), 80-91.

[25] V. O. Vakhnenko, E. J. Parkes and A. J. Mprrison, A BĂ„acklund transformation and the inverse scattering transformation method for the generalized Vakhnenko equation, Chaos, Solitons and Fractals 17 (2003), 683-692.

[26] M. Wang, Y. Zhou and Z. Li, Applications of homogeneous balance method to exact solution of nonlinear equations in mathematical physics, Physics Letters A 216 (1996), 67-75.

[27] G. Whitham Waves, Wiley, Linear and Nonlinear, New York, 1974.