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Exp-function method for nonlinear wave equations. (English) Zbl 1141.35448
Summary: A new method, called Exp-function method, is proposed to seek solitary solutions, periodic solutions and compacton-like solutions of nonlinear differential equations. The modified KdV equation and Dodd-Bullough-Mikhailov equation are chosen to illustrate the effectiveness and convenience of the suggested method.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
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References:
[1] Abdusalam, H. A.: On an improved complex tanh-function method. Int J nonlinear sci numer simul 6, No. 2, 99-106 (2005)
[2] Zayed, E. M. E.; Zedan, H. A.; Gepreel, K. A.: Group analysis and modified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear Euler equations. Int J nonlinear sci numer simul 5, No. 3, 221-234 (2004)
[3] Bai, C. L.; Zhao, H.: Generalized extended tanh-function method and its application. Chaos, solitons & fractals 27, No. 4, 1026-1035 (2006) · Zbl 1088.35534
[4] Wazwaz, A. M.: The tanh method: solitons and periodic solutions for the dodd-bullough-Mikhailov and the tzitzeica-dodd-bullough equations. Chaos, solitons & fractals 25, No. 1, 55-63 (2005) · Zbl 1070.35076
[5] Li, D. S.; Gao, F.; Zhang, H. Q.: Solving the (2+1)-dimensional higher order Broer-Kaup system via a transformation and tanh-function method. Chaos, solitons & fractals 20, No. 5, 1021-1025 (2004) · Zbl 1049.35157
[6] Khuri, S. A.: A complex tanh-function method applied to nonlinear equations of schroedinger type. Chaos, solitons & fractals 20, No. 5, 1037-1040 (2004) · Zbl 1049.35156
[7] Yomba, E.: The modified extended Fan sub-equation method and its application to the (2+1)-dimensional Broer-Kaup-kupershmidt equation. Chaos, solitons & fractals 27, No. 1, 187-196 (2006) · Zbl 1088.35532
[8] Ren, Y. J.; Zhang, H. Q.: 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, No. 4, 959-979 (2006) · Zbl 1088.35536
[9] Wang, D. S.; Zhang, H. Q.: Further improved F-expansion method and new exact solutions of konopelchenko-dubrovsky equation. Chaos, solitons & fractals 25, No. 3, 601-610 (2005) · Zbl 1083.35122
[10] Dai, C. Q.; Zhang, J. F.: Jacobian elliptic function method for nonlinear differential-difference equations. Chaos, solitons & fractals 27, No. 4, 1042-1047 (2006) · Zbl 1091.34538
[11] Yu, Y. X.; Wang, Q.; Zhang, H. Q.: The extended Jacobi elliptic function method to solve a generalized Hirota-satsuma coupled KdV equations. Chaos, solitons & fractals 26, No. 5, 1415-1421 (2005) · Zbl 1106.35087
[12] Zhao, X. Q.; Zhi, H. Y.; Zhang, H. Q.: Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Itô system. Chaos, solitons & fractals 28, No. 1, 112-126 (2006) · Zbl 1134.35301
[13] He, J. H.; Wu, X. H.: Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, solitons & fractals 29, No. 1, 108-113 (2006) · Zbl 1147.35338
[14] Momani, S.; Abuasad, S.: Application of he’s variational iteration method to Helmholtz equation. Chaos, solitons & fractals 27, No. 5, 1119-1123 (2006) · Zbl 1086.65113
[15] Abassy, T. A.; El-Tawil, M. A.; Saleh, H. K.: The solution of KdV and mkdv equations using Adomian Padé approximation. Int J nonlinear sci numer simul 5, No. 4, 327-339 (2004)
[16] El-Sayed, S. M.; Kaya, D.; Zarea, S.: The decomposition method applied to solve high-order linear Volterra-Fredholm integro-differential equations. Int J nonlinear sci numer simul 5, No. 2, 105-112 (2004)
[17] El-Danaf, T. S.; Ramadan, M. A.; Alaal, F. E. I.A.: The use of Adomian decomposition method for solving the regularized long-wave equation. Chaos, solitons & fractals 26, No. 3, 747-757 (2005) · Zbl 1073.35010
[18] Zhu, Y. G.; Chang, Q. S.; Wu, S. C.: Construction of exact solitary solutions for Boussinesq-like $B(m,n)$ equations with fully nonlinear dispersion by the decomposition method. Chaos, solitons & fractals 26, No. 3, 897-903 (2005) · Zbl 1080.35097
[19] Liu, H. M.: Generalized variational principles for ion acoustic plasma waves by he’s semi-inverse method. Chaos, solitons & fractals 23, No. 2, 573-576 (2005) · Zbl 1135.76597
[20] Liu, H. M.: Variational approach to nonlinear electrochemical system. Int J nonlinear sci numer simul 5, No. 1, 95-96 (2004)
[21] Zhang, J.; Yu, J. Y.; Pan, N.: Variational principles for nonlinear fiber optics. Chaos, solitons & fractals 24, No. 1, 309-311 (2005) · Zbl 1135.78330
[22] He, J. H.: Application of homotopy perturbation method to nonlinear wave equations. Chaos, solitons & fractals 26, No. 3, 695-700 (2005) · Zbl 1072.35502
[23] He, J. H.: Homotopy perturbation method for bifurcation of nonlinear problems. Int J nonlinear sci numer simul 6, No. 2, 207-208 (2005)
[24] El-Shahed, M.: Application of he’s homotopy perturbation method to Volterra’s integro-differential equation. Int J nonlinear sci numer simul 6, No. 2, 163-168 (2005)
[25] Rosenau, P.; Hyman, J. M.: Compactons: solitons with finite wavelengths. Phys rev lett 75, No. 5, 564-567 (1993) · Zbl 0952.35502
[26] Rosenau, P.: Compact and noncompact dispersive patterns. Phys lett A 275, No. 3, 193-203 (2000) · Zbl 1115.35365
[27] Wazwaz, A. M.: Two reliable methods for solving variants of the KdV equation with compact and noncompact structures. Chaos, solitons & fractals 28, No. 2, 454-462 (2006) · Zbl 1084.35079
[28] Zhu, Y.; Gao, X.: Exact special solitary solutions with compact support for the nonlinear dispersive $K(m,n)$ equations. Chaos, solitons & fractals 27, No. 2, 487-493 (2006) · Zbl 1088.35547
[29] Zhu, Y.; Chang, Q.; Wu, S.: Exact solitary-wave solutions with compact support for the modified KdV equation. Chaos, solitons & fractals 24, No. 1, 365-369 (2005) · Zbl 1067.35099