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Lax Pair

A pair of linear Operators $L$ and $A$ 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 $L$ and $A$ corresponding to a given equation, so it is actually simpler to postulate a given $L$ and $A$ 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.

© 1996-9 Eric W. Weisstein