Euler Equations Related to the Generalized Neveu-Schwarz Algebra
Dafeng Zuo
TL;DR
This paper explores supersymmetric Euler equations linked to the generalized Neveu-Schwarz algebra, deriving new integrable systems and their Hamiltonian structures, expanding the landscape of supersymmetric integrable models.
Contribution
It introduces several new supersymmetric and bi-superhamiltonian generalizations of known integrable systems based on the generalized Neveu-Schwarz algebra.
Findings
New supersymmetric generalizations of the coupled KdV, Camassa-Holm, and Hunter-Saxton equations.
Identification of bi-superhamiltonian structures for these systems.
Most of these generalizations are novel contributions to the field.
Abstract
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.
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