MOTION OF CURVES AND SURFACES AND NONLINEAR EVOLUTION-EQUATIONS IN (2-DIMENSIONS(1))

It is shown that a class of important integrable nonlinear evolution e quations in (2 + 1) dimensions can be associated with the motion of sp ace curves endowed with an extra spatial variable or equivalently, mov ing surfaces. Geometrical invariants then define topological conserved quantities. Underlying evolution equations are shown to be associated with a triad of linear equations. Our examples include Ishimori equat ion and Myrzakulov equations which are shown to be geometrically equiv alent to Davey-Stewartson and Zakharov-Strachan (2 + 1) dimensional no nlinear Schrodinger equations, respectively. (C) 1998 American Institu te of Physics. [S0022-2488(98)02006-4].