Lax pair and super-Yangian symmetry of the non-linear super-Schrödinger equation

V. Caudrelier; E. Ragoucy

doi:10.1063/1.1625078

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arXiv · math/0306115

Lax pair and super-Yangian symmetry of the non-linear super-Schrödinger equation

V. Caudrelier·E. Ragoucy

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Abstract

We consider a version of the non-linear Schrödinger equation with M bosons and N fermions. We first solve the classical and quantum versions of this equation, using a super-Zamolodchikov-Faddeev (ZF) algebra. Then we prove that the hierarchy associated to this model admits a super-Yangian Y(gl(M|N)) symmetry. We exhibit the corresponding (classical and quantum) Lax pairs. Finally, we construct explicitly the super-Yangian generators, in terms of the canonical fields on the one hand, and in terms of the ZF algebra generators on the other hand. The latter construction uses the well-bred operators introduced recently.

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BibTeX RIS

V. Caudrelier, E. Ragoucy. 2003-06-06. Lax pair and super-Yangian symmetry of the non-linear super-Schrödinger equation. https://doi.org/10.1063/1.1625078

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