  This work concerns soliton-type numerical solutions for two
Whitham-Boussinesq-type models. Solitary waves are computed using an iterative
Newton-type and continuation methods with high accuracy. The method allow us to
compute solitary waves with large amplitude and speed close to the singular
limit. These solitary waves are set as initial data and overtaking collisions
are considered for both systems. We show that both system satisfy the geometric
Lax-categorization of two-soliton collision. Numerical evidences indicate that
one of the systems also admits an algebraic Lax-categorization based on the
ratio of the initial solitary wave amplitudes with a different range from the
one predicted by Lax. However, we show that such categorization is not possible
for the second system.
