Determination of the coastal rate of erosion for the rivers with sandy bottom

We propose a mathematical model for a coastal slope development of a plains river with a sandy bottom. To determine the transportation of bed sediments the original analytical law, which does not contain phenomenological parameters has been used. To solve the problem we suggest splitting the computational domain into two subregions according to the dominant mechanisms of deformation of the bottom. We have obtained an asymptotic formula, which determines the rate of retreat for the coastal slope, and accurate to the factor complies with the empirical formula of L. I. Vikulova.