Li, Jibin; Zhang, Yi Exact M/W-shape solitary wave solutions determined by a singular traveling wave equation. (English) Zbl 1162.35341 Nonlinear Anal., Real World Appl. 10, No. 3, 1797-1802 (2009). Summary: It had been found that some nonlinear wave equations have the so-called “W/M”-shape-peaks solitons. What is the dynamical behavior of these solutions? To answer this question, all traveling wave solutions in the parameter space are investigated for a integrable water wave equation from a dynamical systems theoretical point of view. Exact explicit parametric representations of all solitary wave solutions are given. Cited in 2 Documents MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:discontinuous planar dynamical system; “W/M”-shape-peaks soliton; periodic wave solution; bifurcation; nonlinear wave equation PDFBibTeX XMLCite \textit{J. Li} and \textit{Y. Zhang}, Nonlinear Anal., Real World Appl. 10, No. 3, 1797--1802 (2009; Zbl 1162.35341) Full Text: DOI References: [1] Byrd, P. F.; Fridman, M. D., Handbook of Elliptic Integrals for Engineers and Scientists (1971), Springer: Springer Berlin · Zbl 0213.16602 [2] Li, J. B.; Dai, H. H., On the Study of Singular Nonlinear Traveling Wave Equations: Dynamical System Approach (2007), Science Press: Science Press Beijing [3] Li, J. B.; Wu, J. H.; Zhu, H. P., Travelling waves for an integrable higher order KdV type wave equations, Int. J. Bifurcation Chaos, 16, 8, 2235-2260 (2006) · Zbl 1192.37100 [4] Qiao, Z. J., A new integrable equation with cuspons and W/M-shape peaks solitons, J. Math. Phys., 47, 112701-112709 (2006) · Zbl 1112.37063 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.