Solving Coupled Hirota System by Using Homotopy Perturbation and Homotopy Analysis Methods

Rostam K. Saeed1 and Rebwar S. Muhammad1

1Salahaddin University, College of Science - Department of Mathematics, Kurdistan Region, Erbil-Iraq,

Abstract

In this paper, two methods, namely Homotopy Perturbation Method

(HPM) and Homotopy Analysis Method (HAM) are applied to obtain approximate

solutions of the nonlinear coupled Hirota system (CHS). We see that these two

methods are efficient and effectives for solving nonlinear CHS and the obtained

results of the two methods coincide with each other. In our work, Maple 13 has

been used for computations.

Key Words: Homotopy Perturbation Method, Homotopy Analysis Method, Coupled Hirota System, analytical solution.

References

[1] Al-Harbi, W. G., Numerical solution of Hirota equation, MSc. Thesis, Umm AL-Qura University-

Faculty of Applied Science for Girls - Department of Mathematics, Kingdom of Saudi Arabia, 2009.

[2] Alomari, A. K., Noorani, M. S. M. and Nazar, R., Comparison between the Homotopy analysis method

and Homotopy perturbation method to solve coupled Schrödinger-KdV equation, J. Appl. Math.

Comput., VOl.(31), pp.1–12. (2009).

[3] He, J-H., Homotopy perturbation technique, Comput. Math. Appl. Mech. Eng., Vol.(178), pp. 257-262.

(1999).

[4] Hirota, R. and Satsuma, J., Soliton solution of the coupled KdV system, Phys. Lett. Vol.(85A), No.8-9,

pp. 407-408. (1981).

[5] Hoseini, S. M. and Marchant, T. R., Solitary wave interaction and evolution for higher-order Hirota

equation, Wave Motion. Vol.(44), pp. 92-106. (2006).

[6] Liao, S., The proposed homotopy analysis method technique for the solution of nonlinear problems,

Ph.D. Thesis, Shanghai Jian Tong University, Shanghai, 1992.

[7] Liao, S., Beyond perturbation: introduction to Homotopy analysis method, modern mechanics and

mathematics, Chapman and Hall/CRC Press, Boca Raton, 2003.

[8] Raslan, K. and Abu Shaeer, Z. F., The tanh methods for the Hirota equations, International Journal of

Computer Applications, Vol.(107), No. (11), pp.5-9. (2014).

[9] Wazwaz, A. M., The tanh and the sine-cosine Methods for the complex modified Kdv equation and the

generalized Kdv equation, Comput. Math, Applic. Vol.(49), pp.1101-1112. (2005).

[10]Zubair,T., Usman M., Ali, U. and Mohyud-Din, S. T., Homotopy analysis method for system of partial

differential equations, International Journal of Modern Engineering Sciences, Vol.(1), No.2, pp.67-79. (2012)

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