Analysis of BBM solitary wave interactions using the conserved quantities

TL;DR

This paper introduces a conserved quantity-based method to analyze BBM solitary wave interactions, offering a fast, accurate alternative to complex PDE solutions for studying wave shape, structure, and interactions.

Contribution

A novel, efficient method utilizing conserved quantities is developed to analyze BBM solitary wave interactions without solving complex nonlinear PDEs.

Findings

Method shows high accuracy compared to numerical solutions.

Applicable for benchmarking and stability analysis of solitary waves.

Effective for different initial wave shapes.

Abstract

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.