Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions

Details Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions

1997-09-20

arxiv.org/abs/solv-int/9709009v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, RevTeX, to appear in J. Math. Phys

Scientific paper

10.1063/1.532466

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.

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