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We study possible factorizations of supersymmetric (SUSY) transformations inthe one-dimensional quantum mechanics into chains of elementary Darbouxtransformations with nonsingular coefficients. A classification of irreducible(almost) isospectral transformations and of related SUSY algebras is presented.The detailed analysis of SUSY algebras and isospectral operators is performedfor the third-order case.

journal of mathematical sciences

Factorization of nonlinear supersymmetry in one-dimensional Quantum  Mechanics. I: general classification of reducibility and analysis of the  third-order algebra