Abstract
We consider a non-isospectral scattering problem having as its spatial part an energy-dependent Schrödinger 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 isospectral scattering problems and include multicomponent extensions of the AKNS equation and also a generalization of the Dym equation. An extension of the Fuchssteiner - Fokas - Camassa - Holm equation to (2 + 1) dimensions is also presented.
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