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

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

2003-06-06

arxiv.org/abs/math/0306115v1

J.Math.Phys. 44 (2003) 5706-5732

Mathematics

Quantum Algebra

32 pages, no figure

Scientific paper

We consider a version of the non-linear Schr\"odinger 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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