Abstract:
It is shown that a class of important integrable nonlinear evolution equations
in (2+1) dimensions can be associated with the motion of space curves
endowed with an extra spatial variable or equivalently, moving 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 equation and Myrzakulov equations which are
shown to be geometrically equivalent to Davey-Stewartson and Zakharov -
Strachan (2+1) dimensional nonlinear Schr¨odinger equations respectively.
