A pair of linear Operators and associated with a given Partial Differential Equation which can be used to solve the equation. However, it turns out to be very difficult to find the and corresponding to a given equation, so it is actually simpler to postulate a given and and determine to which Partial Differential Equation they correspond (Infeld and Rowlands 1990).
See also Partial Differential Equation
Infeld, E. and Rowlands, G. ``Integrable Equations in Two Space Dimensions as Treated by the Zakharov Shabat Methods.''
§7.10 in Nonlinear Waves, Solitons, and Chaos. Cambridge, England: Cambridge University Press, pp. 216-223, 1990.