Integrability of S-deformable surfaces: conservation laws, Hamiltonian structures and more

TL;DR

This paper investigates the integrability properties of S-deformable surfaces, revealing their rich mathematical structure through conservation laws, Hamiltonian frameworks, and recursion operators.

Contribution

It introduces infinitely many nonlocal conservation laws, compatible Hamiltonian structures, and a recursion operator for the deformation equations of S-deformable surfaces.

Findings

Existence of infinitely many nonlocal conservation laws.

Identification of compatible local Hamiltonian structures.

Development of a recursion operator for the deformation equations.

Abstract

We present infinitely many nonlocal conservation laws, a pair of compatible local Hamiltonian structures and a recursion operator for the equations describing surfaces in three-dimensional space that admit nontrivial deformations which preserve both principal directions and principal curvatures (or, equivalently, the shape operator).