×

zbMATH — the first resource for mathematics

A note on the “Exp-function method for traveling waves of nonlinear evolution equations”. (English) Zbl 1245.65139
Summary: We analyze the paper of M. A. Noor et al. [Appl. Math. Comput. 216, No. 2, 477–483 (2010; Zbl 1187.65115)]. Using the Exp-function method Noor et al. found the “generalized solitary and periodic solutions” of Zakharov-Kuznetsov and Zakharov-Kuznetsov-Modified-Equal-Width equations. We have checked Noor’s solutions and proved that seven from ten of them does not satisfy to equations considered. The general solution of the Zakharov-Kuznetsov equation in the traveling waves was obtained along ago. We give this solutions in this letter for the reference source.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Noor, Muhammad Aslam; Mohyud-Din, Syed Tauseef; Waheed, Asif; Al-Said, Eisa A., Exp-function method for traveling waves of nonlinear evolution equations, Appl. math. comput., 216, 477-483, (2010) · Zbl 1187.65115
[2] Davis, H.T., Introduction to nonlinear differential and integral equations, (1962), Dover New York
[3] Polyanin, A.D.; Zaitsev, V.F., Handbook of exact solutions for ordinary differential equations, (2003), CRC Press Boca Raton, New York, 783 p · Zbl 1024.35001
[4] Tabor, M., Chaos and integrability in nonlinear dynamics: an introduction, (1989), Wiley New York · Zbl 0682.58003
[5] Kudryashov, N.A.; Loguinova, N.B., Be careful with exp-function method, Commun. nonlinear sci. numer. simulat., 14, 1881-1890, (2009) · Zbl 1221.35344
[6] Kudryashov, N.A., Seven common errors in finding exact solutions of nonlinear differential equations, Commun. nonlinear. sci. numer. simulat., 14, 3503-3529, (2009) · Zbl 1221.35342
[7] Kudryashov, N.A.; Ryabov, P.N.; Sinelshchikov, D.I., A note on new kink-shaped solutions and periodic wave solutions for the (2+1)-dimensional sine-Gordon equation, Appl. math. comput., 216, 2479-2481, (2010) · Zbl 1200.35262
[8] Kudryashov, N.A.; Soukharev, M.B., Popular ansatz methods and solitary wave solutions of the kuramoto – sivashinsky equation, Reg. chaotic dynam., 14, 407-419, (2009) · Zbl 1229.34008
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.