A supersymmetric equation associated with a continuum limit of the classical superalgebra sl(n/n+1) is constructed. This equation can be considered as a superextension of a continuous limit of t the Toda lattice with fixed end-points or, in other words, as a supersymmetric version of the heavenly equation. A solution of the Cauchy problem for the continuous limit of the Toda lattice and for its superextension is given using some formal reasonings.
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Saveliev, M.V., Sorba, P. Solution of the Cauchy problem for a continuous limit of the Toda lattice and its superextension. Lett Math Phys 22, 119–122 (1991). https://doi.org/10.1007/BF00405175
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