The classical treatment of the surface transformations which provide the
origins of Backlund theory is .to be found in the work of Lie [103, 104] and
Backlund [1-5]. The subject was subsequently developed by both Goursat
[105] and Clairin [106]. The modern interest in Backlund transformations
lies in that they may be used in one of two important ways in connection
with integral surfaces of certain nonlinear partial differential equations. Thus,
invariance under a Backlund transformation may be used, under appropriate
circumstances, to generate an infinite sequence of solutions of such equations
by a purely algebraic superposition principle. On the other hand, Backlund
transformations may sometimes be adduced to link nonlinear equations to
canonical forms whose properties are well established.
