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).
Lax Pair
See also
Partial Differential EquationExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Lax PairCite this as:
Weisstein, Eric W. "Lax Pair." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LaxPair.html