Lax Triples for Integrable Surfaces in Three-Dimensional Space

Abstract EN

We study Lax triples (i.e., Lax representations consisting of three linear equations) associated with families of surfaces immersed in three-dimensional Euclidean space E 3 .

We begin with a natural integrable deformation of the principal chiral model.

Then, we show that all deformations linear in the spectral parameter λ are trivial unless we admit Lax representations in a larger space.

We present an explicit example of triply orthogonal systems with Lax representation in the group S p i n ( 6 ) .

Finally, the obtained results are interpreted in the context of the soliton surfaces approach.