PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation

Abstract

We discuss several PT-symmetric deformations of superderivatives. Based on these various possibilities, we propose new families of complex PT-symmetric deformations of the supersymmetric Korteweg-de Vries equation. Some of these new models are mere fermionic extensions of the former in the sense that they are formulated in terms of superspace valued superfields containing bosonic and fermionic fields, breaking however the supersymmetry invariance. Nonetheless, we also find extensions, which may be viewed as new supersymmetric Korteweg-de Vries equation. Moreover, we show that these deformations allow for a non-Hermitian Hamiltonian formulation and construct three charges associated to the corresponding flow.

arXiv comment10 pages

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Cited by in corpus (9)

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• Probability Density in the Complex Plane
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• Conduction bands in classical periodic potentials
• Periodic orbits for classical particles having complex energy
• Integrable models from PT-symmetric deformations
• PT-symmetry in quasi-integrable models