Xiong, Shulin An analytic solution of Burgers-KdV equation. (English) Zbl 0704.35126 Chin. Sci. Bull. 34, No. 14, 1158-1162 (1989). Some authors proposed successively Burgers-KdV equation (1) when they studied flow of liquid containing small bubbles, flow of fluid in an elastic tube and other problems: \[ (1)\quad U_ t+U\cdot U_ x-\nu U_{xx}+\delta U_{xxx}=0, \] where \(\nu\) and \(\delta\) are diffusion and dispersion factors, respectively. In the present work, a class of solution to (1) which has a simple form containing exponential functions is found, and the construction of shock waves expressed by this solution is analysed. Reviewer: H.Haruki Cited in 13 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35C05 Solutions to PDEs in closed form Keywords:Burgers-KdV equation; exponential functions; shock waves PDFBibTeX XMLCite \textit{S. Xiong}, Chin. Sci. Bull. 34, No. 14, 1158--1162 (1989; Zbl 0704.35126)