BOUSSINESQ SOLITARY-WAVE AS A MULTIPLE-TIME SOLUTION OF THE KORTEWEG-DE VRIES HIERARCHY

We study the Boussinesq equation from the point of view of a multiple- time reductive perturbation method. As a consequence of the eliminatio n of the secular producing terms through the use of the Korteweg-de Vr ies hierarchy, we show that the solitary-wave of the Boussinesq equati on is a solitary-wave satisfying simultaneously all equations of the K orteweg-de Vries hierarchy, each one in an appropriate slow time varia ble. (C) 1995 American Institute of Physics.