Abstract: The importance of the inverse scattering problem for the Schrödinger equation with energy-dependent potential:
y"={ζ²-[u(x)+ζv(x)]}y=0 (1) has been noticed by quite a few authors. Jaulent and Miodek^[1] have used it to solve some nonlinear evolution equations with isospectral condition ζ_t=0. Li and Zhuang^[2,3] have further made use of (1) to expand the solvable class of nonlinear evolution equations. Several physical problems in absorption media can be reduced to the inverse scattoring problem of(1) (see[4]).