  In this paper, a simple, robust, fast and effective method based on the
conserved quantities is developed to approximate and analyse the shape,
structure and interaction characters of the solitary waves described by the
Benjamin-Bona-Mahony (BBM) equation. Due to the invariant character of the
conserved quantities, there is no need to solve the related complex nonlinear
partial differential BBM equation to simulate the interactions between the
solitary waves at the most merging instance. Good accuracy of the proposed
method has been found when compared with the numerical method for the solitary
wave interactions with different initial incoming wave shapes. The conserved
quantity method developed in this work can serve as an ideal tool to benchmark
numerical solvers, to perform the stability analysis, and to analyse the
interacting phenomena between solitary waves.
