Lax Pair

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 2000).

REFERENCES:

Infeld, E. and Rowlands, G. "Integrable Equations in Two Space Dimensions as Treated by the Zakharov-Shabat Method." §7.10 in Nonlinear Waves, Solitons, and Chaos, 2nd ed. Cambridge, England: Cambridge University Press, pp. 192-199, 2000.