An analytic solution of Burgers-KdV equation (Q916914)

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.