The Korteweg-de Vries type of equation (called KdV-top) for uni-directional waves over a slowly varying bottom that has been derived by Van Groesen and Pudjaprasetya [E. van Groesen, S.R. Pudjaprasetya, Uni-directional waves over slowly varying bottom. Part I. Derivation of a KdV-type of equation, Wave Motion 18 (1993) 345¿370.] is used to describe the splitting of solitary waves, running over shallower water, into two (or more) waves. Results of numerical computations with KdV-top are presented; qualitative and quantitative comparisons between the analytical and numerical results show a good agreement.
Pudjaprasetya, S. R., Pudjaprasetya, S. R., van Groesen, E. W. C., & Soewono, E. (1999). The splitting of solitary waves over shallower water. Wave motion, 29(29), 375-389. https://doi.org/10.1016/S0165-2125(98)00040-7