Generalized Nonlocal Symmetries of Two-Component Camassa–Holm and Hunter–Saxton Systems

Abstract

The two-component Camassa–Holm system and two-component Hunter–Saxton system are completely integrable models. In this paper, it is shown that these systems admit nonlocal symmetries by their geometric integrability. As an application, we obtain the recursion operator and conservation laws by using this kind of nonlocal symmetries.

Keywords

• nonlocal symmetries
• two-component Camassa–Holm system
• two-component Hunter–Saxton system
• integrability property