Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 9 (2013), 045, 12 pages      arXiv:1306.3628

Euler Equations Related to the Generalized Neveu-Schwarz Algebra

Dafeng Zuo a, b
a) School of Mathematical Science, University of Science and Technology of China, Hefei 230026, P.R. China
b) Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, P.R. China

Received March 11, 2013, in final form June 12, 2013; Published online June 16, 2013

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.

Key words: supersymmetric; bi-superhamiltonian; Euler equations; generalized Neveu-Schwarz algebra.

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