Euler Equations Related to the Generalized Neveu–Schwarz Algebra

In this paper, we study supersymmetric or bi-superhamiltonian Euler equations related to the generalized Neveu–Schwarz algebra. As an application, we obtain several supersymmetric or bi-superhamiltonian generalizations of some well-known integrable systems including the coupled KdV equation, the 2-component Camassa–Holm equation and the 2-component Hunter–Saxton equation. To our knowledge, most of them are new.