Liu, Xiqiang; Bai, Chenglin Exact solutions of some fifth-order nonlinear equations. (English) Zbl 0954.35143 Appl. Math., Ser. B (Engl. Ed.) 15, No. 1, 28-32 (2000). Summary: To solve the nonlinear partial differential equations is changed into solving some algebraic equations by using the function \(U\) to be expressed as linear independent functions. The new soliton and periodic solutions of some fifth-order nonlinear partial differential equations \[ U_t+\alpha U^2U_x-\beta U_x U_{xx}-\gamma UU_{xxx}+ sU_{xxxxx}= 0 \] are obtained. Cited in 4 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 35C05 Solutions to PDEs in closed form Keywords:soliton; periodic solutions PDF BibTeX XML Cite \textit{X. Liu} and \textit{C. Bai}, Appl. Math., Ser. B (Engl. Ed.) 15, No. 1, 28--32 (2000; Zbl 0954.35143) Full Text: DOI References: [1] Drazin, P. G., Johnson, R. S., Solitons: an Introduction, Cambridge University Press, New York, 1989. · Zbl 0661.35001 [2] Han Ping, Lou Senyue, New exact solutions of the Kaup-Kupershmidt equation related to a non-local symmetry, Acta Physica Sinica, 1997, 46(7): 1250–1253. [3] Lou Senyue, Twelve sets of symmetries of the Caudrey-Dodd-Gibbon-Sawada-Kotera equation, Phys. Lett. A, 1993, 175: 23–26. 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.