MULTICOMPONENT EQUATIONS ASSOCIATED TO NONISOSPECTRAL SCATTERING PROBLEMS

We consider a non-isospectral scattering problem having as its spatial part an energy-dependent Schrodinger operator. This gives rise to new completely integrable multicomponent systems of equations in (2 + 1) dimensions. Their reductions to systems in (1 + 1) dimensions have iso spectral scattering problems and include multicomponent extensions of the AKNS equation and also a generalization of the Dym equation. An ex tension of the Fuchssteiner-Fokas-Camassa-Holm equation to (2 + 1) dim ensions is also presented.