Solving the hierarchy of the nonisospectral KdV equation with self-consistent sources via the inverse scattering transform

Abstract

The hierarchy of the nonisospectral KdV equation with self-consistent sources is derived. N-soliton solutions of the hierarchy are obtained through the inverse scattering transform. We develop new treatment of singularities appearing in the Lax pair in the process of determining time revolutions of scattering data. Our approach is general and can apply to other (1 + 1)-dimensional nonisospectral soliton hierarchy with self-consistent sources.