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

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).

Minor revision

References in corpus (4)

• A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems
• A simple way of making a Hamiltonian system into a bi-Hamiltonian one
• Hamiltonian structures for general PDEs
• Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility

Cited by in corpus (2)

• Nonlocal conservation laws of the constant astigmatism equation
• Integrability of anti-self-dual vacuum Einstein equations with nonzero cosmological constant: an infinite hierarchy of nonlocal conservation laws