Asymptotic behaviour as $t\to \infty$ of the solutions of the generalized Korteweg–de Vries equation

Asymptotic formulae representing for large time the solution of the Cauchy problem are obtained for the generalized Korteweg–de Vries equation with non-linear term to an integer power greater than three. The error terms are estimated. The method is based on the perturbation theory with respect to a parameter characterizing the smallness of the initial data.