  In this letter, a definition of the higher dimensional Lax pair for a lower
dimensional system which may be a chaotic system is given. A special concrete
(2+1)-dimensional Lax pair for a general (1+1)-dimensional three order
autonomous partial differential equation is studied. The result shows that any
(1+1)-dimensional three order semi-linear autonomous system (no matter it is
integrable or not) possesses infinitely many (2+1)-dimensional Lax pairs.
Especially, every solution of the KdV equation and the Harry-Dym equation with
their space variable being replaced by the field variable can be used to obtain
a (2+1)-dimensional Lax pair of any three order (1+1)-dimensional semi-linear
equation.

Pattern Formation and Solitons;Chaotic Dynamics