THE ZAKHAROV-SHABAT INVERSE SPECTRAL PROBLEM FOR OPERATORS

Many soliton equations, their solutions and their properties, can be d educed from simpler (essentially linear) equations involving more comp licated objects, e.g., integral operators. The deduction process from the operator-valued equation to the scalar one amounts to some rather simple procedure like taking a trace or a determinant. This is describ ed for the class of soliton equations solvable with the Zakharov-Shaba t spectral transform.