A Direct Linearization Method of the Non-Isospectral KdV Equation

Direct linearization method is used to solve the non-isospectral KdV equation. The corresponding singular linear integral equation and the time dependence of measure in the singular linear integral equation are proposed. Furthermore, the solutions to the non-isospectral modified KdV equation are also derived by using the singular linear integral equation of the non-isospectral KdV equation.