Wazwaz, Abdul-Majid The tanh method for traveling wave solutions of nonlinear equations. (English) Zbl 1054.65106 Appl. Math. Comput. 154, No. 3, 713-723 (2004). Summary: We employ the tanh method for traveling wave solutions of nonlinear equations. The study is extended to equations that do not have tanh polynomial solutions. The efficiency of the method is demonstrated by applying it for a variety of selected equations. Cited in 1 ReviewCited in 181 Documents MSC: 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35Q53 KdV equations (Korteweg-de Vries equations) Keywords:tanh method; traveling wave solutions; Korteweg-de Vries equation; KdV equation; Fisher’s equation; numerical examples Software:ATFM PDF BibTeX XML Cite \textit{A.-M. Wazwaz}, Appl. Math. Comput. 154, No. 3, 713--723 (2004; Zbl 1054.65106) Full Text: DOI OpenURL References: [1] Malfliet, W, Solitary wave solutions of nonlinear wave equations, Am. J. phys., 60, 7, 650-654, (1992) · Zbl 1219.35246 [2] Malfliet, W, The tanh method: I. exact solutions of nonlinear evolution and wave equations, Physica scripta, 54, 563-568, (1996) · Zbl 0942.35034 [3] Malfliet, W, The tanh method: II. perturbation technique for conservative systems, Physica scripta, 54, 569-575, (1996) · Zbl 0942.35035 [4] Khater, A.H; Malfliet, W; Callebaut, D.K; Kamel, E.S, The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction – diffusion equations, Chaos soliton. fract., 14, 513-522, (2002) · Zbl 1002.35066 [5] Parkes, E.J; Duffy, B.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 [6] Fan, E; Hon, Y.C, Generalized tanh method extended to special types of nonlinear equations, Z. naturforsch, 57a, 692-700, (2002) [7] Glasner, K, Nonlinear preconditioning for diffuse interfaces, J. comput. phys., 174, 695-711, (2001) · Zbl 0991.65076 [8] Kawahara, T; Tanaka, M, Interactions of traveling fronts: an exact solution of a nonlinear diffusion equation, Phys. lett., 97A, 8, 311-314, (1983) [9] Conte, R; Mussette, M, Link between solitary waves and projective Riccati equations, J. phys.: math. gen., 25, 5609-5623, (1992) · Zbl 0782.35065 [10] Huibin, L; Kelin, W, Exact solutions for two nonlinear equations: I, J. phys. A: math. gen., 23, 3923-3928, (1990) · Zbl 0718.35020 [11] Wang, M, Exact solutions for a compound kdv – burgers equation, Phys. lett. A, 213, 279-287, (1998) · Zbl 0972.35526 [12] Ma, W, Travelling wave solutions to a seventh order generalized KdV equation, Phys. lett. A, 180, 221-224, (1993) [13] Wazwaz, A.M, Partial differential equations: methods and applications, (2002), Balkema The Netherlands · Zbl 0997.35083 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.