Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III

Abstract A unified treatment of monodromy and spectrum preserving deformations is presented. In particular a general procedure is described to reduce the latter into the former consistently. The concept of the τ-function, previously introduced for the former [2], is extended to the isospectral context. It is shown that the general monodromy and spectrum preserving deformation equations can be written as Hirota's bilinear differential equations by using the τ-functions as dependent variables.

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