A HIROTA BILINEAR METHOD FOR A COMPLEX PERTURBED MODIfiED KORTEWEG-DE VRIES EQUATION
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soliton solution, Schrodinger-Hirota equation, nonlinear equations, Hirota direct method.##article.abstract##
In this paper by using Hirota direct method, the one-soliton solution of perturbed modified Korteweg-de Vries equation mKdV are studied. We have shown the evolution of the one-soliton solutions.
##submission.citations##
1. M.J. Ablowitz, H. Segur H. Solitons and Inverse Scattering Transform, SIAM,
Philadelphia,1981.
2. W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60,
pp. 650–654, 1992.
3. W. Malfliet, W. Hereman, The tanh method: I. Exact solutions of nonlinear evolution
and waveequations, Phys. Scr., 54, pp. 563–568, 1996. 4. A.M. Wazwaz, The tanh method for travelling wave solutions of nonlinear
equations, Appl.Math. Comput., 154(3), pp. 713–723, 2004.
5. S.A. El-Wakil, M.A. Abdou, New exact travelling wave solutions using modified
extended tanh-function method, Chaos Solitons Fractals, 31(4), pp. 840–852, 2007.
6. E. Fan, Extended tanh-function method and its applications to nonlinear equations,
Phys. Lett. A, 277(4–5), pp. 212–218, 2000.
7. A.M. Wazwaz, The extended tanh method for abundant solitary wave solutions of
nonlinear wave equations, Appl. Math. Comput., 187(2), pp. 1131–1142, 2007.
8. A.M. Wazwaz, Exact solutions to the double sinh-gordon equation by the tanh
method and a variable separated ODE method, Comput. Math. Appl., 50(10–11), pp.
1685–1696, 2005.
9. A.M. Wazwaz, A sine-cosine method for handling nonlinear wave equations, Math.
Comput. Modelling, 40, pp. 499–508, 2004.
10. C. Yan, A simple transformation for nonlinear waves, Phys. Lett. A, 224(1–2), pp.
77–84, 1996.
11. E. Fan, H. Zhang, A note on the homogeneous balance method, Phys. Lett. A, 246,
pp. 403–406, 1998.
12. M.L. Wang, Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A,
213(5–6), pp. 279–287, 1996.
13. C.Q. Dai, J.F. Zhang, Jacobian elliptic function method for nonlinear differential
difference equations, Chaos Solitons Fractals, 27, pp. 1042–1049, 2006.
14. E. Fan, J. Zhang, Applications of the Jacobi elliptic function method to special-type
nonlinear equations, Phys. Lett. A, 305, pp. 383–392, 2002.
15. S. Liu, Z. Fu, S. Liu, Q. Zhao, Jacobi elliptic function expansion method and
periodic wave solutions of nonlinear wave equations, Phys. Lett. A, 289(1–2), pp. 69
74, 2001.
16. X.Q. Zhao, H.Y. Zhi, H.Q. Zhang, Improved Jacobi-function method with
symbolic computation to construct new double-periodic solutions for the generalized
Ito system, Chaos Solitons Fractals, 28, pp. 112–126, 2006. 17. M.A. Abdou, The extended F -expansion method and its application for a class of
nonlinear evolution equations, Chaos Solitons Fractals, 31, pp. 95–104, 2007.
18. Y.J. Ren, H.Q. Zhang, A generalized F -expansion method to find abundant
families of Jacobi elliptic function solutions of the (2 + 1)-dimensional Nizhnik
Novikov–Veselov equation,
Chaos Solitons Fractals, 27, pp. 959–979, 2006.
19. J.L. Zhang, M.L. Wang, Y.M. Wang, Z.D. Fang, The improved F -expansion
method and its applications, Phys. Lett. A, 350(1–2), pp. 103–109, 2006.
20. J.H. He, X.H. Wu, Exp-function method for nonlinear wave equations, Chaos
Solitons Fractals, 30, pp. 700–708, 2006.
21. H. Aminikhah, H. Moosaei, M. Hajipour, Exact solutions for nonlinear partial
differential equations via Exp-function method, Numer. Methods Partial Differ.
Equations, 26(6), pp. 1427–1433, 2009.
22. Z.Y. Zhang, New exact traveling wave solutions for the nonlinear Klein–Gordon
equation, Turk. J. Phys., 32, pp. 235–240, 2008.
23. M.L. Wang, J.L. Zhang, X.Z. Li, The (G’/G)-expansion method and travelling
wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett.
A, 372, pp. 417–423, 2008.
24. S. Zhang, J.L. Tong, W. Wang, A generalized (G’/G)-expansion method for the
mKdV equation with variable coefficients, Phys. Lett. A, 372, pp. 2254–2257, 2008
25. X.B. Hu, W.X. Ma, Phys. Lett. A 293 (2002) 161–165
26. Y.J. Zhang, C.Y. Yang, W.T. Yu, M.L. Liu, G.L. Ma, W.J. Liu, Opt. Quantum
Electron.50 (2018) 295.
27. C.Y. Yang, W.Y. Li, W.T. Yu, M.L. Liu, Y.J. Zhang, G.M. Ma, W.J. Liu, Nonlinear
Dyn. 92 (2018) 203–213.
28. Y.Y. Wang, C.Q. Dai, Y.Q. Xu, J. Zheng, Y. Fan, Nonlinear Dyn. 92 (2018) 1261
1269.29. A.A. Reyimberganov, I.D. Rakhimov, Numerical-analytical solutions of the
nonlinear Schrödinger equation. Taurida Journal of Computer Science Theory and
Mathematics, 80-91
30. G.U. Urazboev, A.A. Reyimberganov, I.D. Rakhimov, Numerical solution of the
system of Marchenko integral equations, Uzbek Mathematical Journal 65 (3), pp. 159
165
31. А. Рейимберганов. Ночизиқли Шредингер тенгламаси учун қўлланиладиган
чекли айирмали схемалар, Илм сарчашмалари, 3-7
