The generalized Weierstrass system and an application to the study of deformations of surfaces by means of integrable hierarchies

摘要

Generalized Weierstrass representations can be used to investigate deformations of surfaces under the action of integrable hierarchies. It will be shown that the generalized Weierstrass representation of Konopelchenko leads to a linear system in a single independent space variable in the case of surfaces of revolution. This result is combined with a second linear problem with an unknown second matrix in terms of a parameter. It is then shown how an integrable hierarchy can be obtained. Solutions to this hierarchy generate deformations which preserve the surface-inducing means of generalized Weierstrass representation.