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

摘要

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