Rui, Weiguo; Chen, Can; Yang, Xinsong; Long, Yao Some new soliton-like solutions and periodic wave solutions with loop or without loop to a generalized KdV equation. (English) Zbl 1203.35242 Appl. Math. Comput. 217, No. 4, 1666-1677 (2010). Summary: By using the integral bifurcation method, we study a generalized KdV equation which was first derived by Fokas from physical considerations via a methodology of Fuchssteiner. All kinds of soliton-like or kink-like wave solutions and periodic wave solutions with loop or without loop are obtained. Smooth compacton-like periodic wave solution and non-smooth periodic cusp wave solution are also obtained. Their dynamic properties are investigated and their profiles are given by mathematical software. Cited in 4 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems 35C08 Soliton solutions 35B10 Periodic solutions to PDEs 35-04 Software, source code, etc. for problems pertaining to partial differential equations Keywords:generalized KdV equation; integral bifurcation method; soliton-like solution; kink-like wave solution; periodic wave solutions with loop PDFBibTeX XMLCite \textit{W. Rui} et al., Appl. Math. Comput. 217, No. 4, 1666--1677 (2010; Zbl 1203.35242) Full Text: DOI References: [1] Fokas, A. S., On a class of physically important integrable equations, Physica D, 87, 145-450 (1995) · Zbl 1194.35363 [2] Fuchssteiner, B.; Fokas, A. 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