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In this paper the non linear differential equation describing the behavior of water surface behind the wave front is obtained by Whit ham method. It is shown that the bed load transport could influence significantly on the stability of the flood wave. In the supercritical flow, the bed load wave will propagate upstream and will linearly stabilize. The different situations when the wave could topple over are analyzed. In the flow without the bed load transport, the results of Whit ham have been reobtained as a special case.  

Whit ham method of the expansion near the wave front propagating on the river with bed load transport