Lax pair and super-Yangian symmetry of the nonlinear super-Schrodinger equation

Caudrelier, V. & Ragoucy, E. (2003). Lax pair and super-Yangian symmetry of the nonlinear super-Schrodinger equation. Journal of Mathematical Physics, 44(12), pp. 5706-5732. doi: 10.1063/1.1625078

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Abstract

We consider a version of the nonlinear Schrodinger 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(Mparallel toN)) 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. (C) 2003 American Institute of Physics.

Item Type: Article
Uncontrolled Keywords: QUANTUM FIELD-THEORY, INVERSE SCATTERING METHOD, EVOLUTION EQUATIONS, MODEL, INTEGRABILITY, CONNECTION, OPERATORS, HIERARCHY, TRANSFORM, SYSTEMS
Subjects: Q Science > QC Physics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/171

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