A bstract Integrability of N = 1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials W(x)=2/x , W(x)=2sinx , and W(x)=2sinhx is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd constants of motion is reduced to finding a triplet of vectors such that all their scalar products can be expressed in terms of the original bosonic first integrals. The supersymmetric generalizations are used to build novel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider three-body systems.
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Anton Galajinsky (2024) studied this question.
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