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,

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. 


[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.
[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)