Yan, Zhenya; Zhang, Hongqing Auto-Bäcklund transformation, multi-soliton solutions and rational fraction solutions for the modified dispersive water waves equations. (Chinese. English summary) Zbl 0961.35147 Acta Math. Sci. (Chin. Ed.) 20, No. 2, 210-215 (2000). Summary: By using Mathematica, an auto-Bäcklund transformation of the modified dispersive water waves equations is obtained, and Darboux transformation between it, the heat equation and a linear equation are derived. Based on these results, multi-soliton solutions, rational fraction solutions and other exact solutions for the equations are found. This way can be also applied to other nonlinear equations. Cited in 2 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction Keywords:modified dispersive water waves equation; auto-Bäcklund transformation; Darboux transformation; exact solution; multi-soliton solution PDFBibTeX XMLCite \textit{Z. Yan} and \textit{H. Zhang}, Acta Math. Sci. (Chin. Ed.) 20, No. 2, 210--215 (2000; Zbl 0961.35147)