RESUMEN

The well-known Kortweg-de Vries equations with the coefficients as two arbitrary functions of the time variable, is studied in this paper. The Painleve property analysis provides the condition on the two variable coefficients, in order to form the lax pairs associated with this equation. The similary analysis shows the non-existence of traveling wave solutions when the equation has variable coefficients. These results are used to show the non-existence of traveling waves in an inhomogeneous medium.