Analytic-bilinear approach to integrable hierarchies. I.Generalized KP hierarchy

Details Analytic-bilinear approach to integrable hierarchies. I.Generalized KP hierarchy Analytic-bilinear approach to integrable hierarchies. I.Generalized KP hierarchy

1996-09-24

arxiv.org/abs/solv-int/9609009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

25 pages, LaTeX

Scientific paper

Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to represent generalized hierarchies of integrable equations in a condensed form of finite functional equations. Resolution of these functional equations leads to the $\tau$-function and addition formulae to it. General discrete transformations of the $\tau$-function are presented in the determinant form. Closed one-form and other formulae also arise naturally within the approach proposed. Generalized KP hierarchy written in terms of different invariants of Combescure symmetry transformations coincides with the usual KP hierarchy and the mKP hierarchy.

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