# Asymptotic soliton like solutions to the singularly perturbed Benjamin-Bona-Mahony equation with variable coefficients

## TL;DR

This paper develops an algorithm to construct asymptotic soliton-like solutions for the variable coefficient Benjamin-Bona-Mahony equation with a small parameter, and proves the accuracy of these solutions.

## Contribution

It introduces a novel algorithm for constructing asymptotic solutions to the BBM equation with variable coefficients and small parameters, with proven accuracy.

## Key findings

- Successfully constructed asymptotic soliton-like solutions.
- Proved theorems on the accuracy of the solutions.
- Enhanced understanding of soliton behavior in variable coefficient BBM equations.

## Abstract

The paper deals with a problem of asymptotic soliton like solutions to the Benjamin-Bona-Mahony (BBM) equaion with a small parameter at the highest derivative and variable coefficients depending on the variables $x$, $t$ as well as a small parameter. There is proposed an algorithm of constructing the solutions and there are proved theorems on accuracy with which the solutions satisfy the BBM equation.