Abstract: There are different forms of the beds on the natural sandy coast, on which the propagation process of the wave is a typical nonlinear one. Based on this, the nonlinear propagation process of the wave on the small-amplitude uneven sloping bed is analyzed by using the perturbation method. After comparing the results of the analytic expression with the correlative experimental data, it shows that the practical situation can be described by the
established evolution model of the wave.

Key words: wave, sandy coast, turning point, semi-linear, singular perturbation, nonlinearity