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This article presents a numerical investigation of overtaking collisionsbetween two solitary waves in the context of the Schamel equation. Our studyreveals different regimes characterized by the behavior of the waveinteractions. In certain regimes, the collisions maintain two well-separatedcrests consistently over time, while in other regimes, the number of localmaxima undergoes variations following the patterns of $2\rightarrow1\rightarrow 2\rightarrow 1\rightarrow 2$ or $2\rightarrow 1\rightarrow 2$.These findings demonstrate that the geometric Lax-categorization observed inthe Korteweg-de Vries equation (KdV) for two-soliton collisions remainsapplicable to the Schamel equation. However, in contrast to the KdV, wedemonstrate that an algebraic Lax-categorization based on the ratio of theinitial solitary wave amplitudes is not feasible for the Schamel equation.Additionally, we show that the statistical moments for two-solitary wavecollisions are qualitatively similar to the KdV equation and the phase shiftsafter soliton interactions are close to ones in integrable KdV and modified KdVmodels.

Investigating overtaking collisions of solitary waves in the Schamel equation