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Extended improved tanh-function method for solving the nonlinear physical problems. (English) Zbl 1165.35046
Summary: By means of the extended improved tanh-function (EITF) method with computerized symbolic computations for constructing new multiple traveling wave solutions for different kinds of nonlinear physical problems are presented and implemented. The solutions for the nonlinear equations such as coupled MKdV, coupled Hirota-Satsuma and coupled KdV equations which include new trigonometric function solutions and rational solutions are exactly obtained.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35C05 Solutions to PDEs in closed form
35A20 Analyticity in context of PDEs
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[1] Ablowitz, M.J., Clarkson, P.A.: Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge (1991) · Zbl 0762.35001
[2] Wadati, M., Sanuki, H., Konno, K.: Relationships among inverse method, Backlund transformation and an infinite number of conservation laws. Program. Theor. Phys. 53, 419–436 (1975) · Zbl 1079.35506
[3] Hirota, R.: Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27, 1192–1194 (1971) · Zbl 1168.35423
[4] Coely, A., et al. (eds.): Backlund and Darboux Transformations. American Mathematical Society, Providence (2001)
[5] Malfeit, W.: Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60, 650–654 (1992) · Zbl 1219.35246
[6] Yan, C.T.: A simple transformation for nonlinear waves. Phys. Lett. A 224, 77–84 (1996) · Zbl 1037.35504
[7] Wang, M.L.: Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213, 279–287 (1996) · Zbl 0972.35526
[8] Yan, Z.Y., Zhang, H.Q.: New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. Phys. Lett. A 285, 355–362 (2001) · Zbl 0969.76518
[9] Yan, Z.Y., Zhang, H.Q.: Auto-Darboux transformation and exact solutions of the brusselator reaction diffusion model. Appl. Math. Mech. 22, 541–546 (2000) · Zbl 0989.92028
[10] Yan, Z.Y., Zhang, H.Q.: New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. Phys. Lett. A 285, 355–362 (2001) · Zbl 0969.76518
[11] Yan, Z.Y.: New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations. Phys. Lett. A 292, 100–106 (2001) · Zbl 1092.35524
[12] Soliman, A.A.: Numerical simulation of the generalized regularized long wave equation by He’s variational iteration method. Math. Comput. Simul. 70(2), 119–124 (2005) · Zbl 1152.65467
[13] Soliman, A.A.: A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations. Chaos Solitons Fractals 29, 294–302 (2006) · Zbl 1099.35521
[14] Abdou, M.A., Soliman, A.A.: New applications of variational iteration method. Physica D 211, 1–8 (2005) · Zbl 1084.35539
[15] Abdou, M.A., Soliman, A.A.: Variational iteration method for solving Burger’s and Coupled Burger’s equations. J. Comput. Appl. Math. 181, 245 (2005) · Zbl 1072.65127
[16] Soliman, A.A., Raslan, K.R.: Collocation method using quadratic B-spline for RLW equation. Int. J. Comput. Math. 78, 399–412 (2001) · Zbl 0990.65116
[17] Soliman, A.A.: Collocation solution of the Korteweg-De Vries equation using septic splines. Int. J. Comput. Math. 81, 325–331 (2004) · Zbl 1058.65113
[18] Soliman, A.A., Hussien, M.H.: Collocation solution for RLW equation with septic spline. Appl. Math. Comput. 161, 623–636 (2005) · Zbl 1061.65102
[19] Yan, Z.: A new sine Gordon equation expansion algorithm to investigate some special nonlinear differential equations. Chaos Solitons Fractals 23, 767–775 (2005) · Zbl 1069.35077
[20] Yan, Z.: The new constructive algorithm and symbolic computation applied to exact solutions of nonlinear wave equations. Phys. Lett. A 331, 193–200 (2004) · Zbl 1123.35348
[21] El-Wakil, S.A., El-Labany, S.K., Zahran, M.A., Sabry, R.: Appl. Math. Comput. 161, 403 (2005) · Zbl 1062.35082
[22] El-Wakil, S.A., El-Labany, S.K., Zahran, M.A., Sabry, R.: Phys. Lett. A 299, 179 (2002) · Zbl 0996.35043
[23] Soliman, A.A.: The modified extended tanh-function method for solving Burgers type equations. Physica A 361(2), 394–404 (2006)
[24] Abdou, M.A., Soliman, A.A.: Modified extended tanh-function method and its application on nonlinear physical equations. Phys. Lett. A 353(6), 487–492 (2006)
[25] Parkes, E.J., Duffy, P.R.: An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput. Phys. Commun. 98, 288–300 (1996) · Zbl 0948.76595
[26] Raslan, K.R.: The decomposition method for a Hirota-Satsuma coupled KdV equation and coupled MKdV equation. Int. J. Comput. Math. 81, 1497–1505 (2004) · Zbl 1064.65118
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