Hirota equations are certain bilinear equations related to integrable models/hierarchies. The dependent variables can, in most cases, be identified with -functions, as it was first observed by Miwa. One often speaks of Hirota’s direct method in solving integrable equations. We say that an equation is put in Hirota bilinear form if it is written as where is the Hirota derivative (or difference) operator. One defines it by
The difference version of Hirota operator is obtained by exponentiating. The Hirota equations enable easier finding of multisoliton? solutions. Recent -systems may also be viewed as a version of generalized Hirota equations.
One can consider partition functions as made up from characters; /characters are by Weyl formula given in terms of (ratios of) certain determinants. Flag minor determinants satisfy bilinear Pluecker relations. If the tau functions are interpreted in terms of infinite Grassmanians (fermionic approach) then the Hirota relations sometimes boil down to Pluecker relations.
Last revised on June 16, 2024 at 16:55:34. See the history of this page for a list of all contributions to it.