  In this paper, we study the possible second order Lax operators for all the
possible (1+1)-dimensional models with Schwarz variants and some special types
of high dimensional models. It is shown that for every (1+1)-dimensional model
and some special types of high dimensional models which possess Schwarz
variants may have a second order Lax pair. The exiplicit Lax pairs for
(1+1)-dimensional Korteweg de Vries equation, Harry Dym equation, Boussinesq
equation, Caudry-Dodd-Gibbon-Sawada-Kortera equation, Kaup-Kupershmidt
equation, Riccati equation, (2+1)-dimensional breaking soliton equation and a
generalized (2+1)-dimensional fifth order equation are given.
