Analysis of BBM solitary wave interactions using the conserved quantities

•Developed a simple approach based on the conserved quantities to analyse the solitary wave interactions described by the Benjamin–Bona–Mahony (BBM) equation.•The main advantage of this approach is that it does not need to solve the nonlinear partial differential BBM equation when simulating the interactions between the solitary waves at the most merging instance.•Good agreement is found between the results of the current method and the numerical results.•This method is ideal to benchmark numerical solvers, perform stability analysis, and analyse soliton interactions for shallow water waves. 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.