Abstract
The remarkable link between the soliton theory and the group GL,,c,was discovered in the early 1980s by Sato [S] and developed, making use of the spinor formalism, by Date, Jimbo, Kashiwara and Miwa [DJKM1,2,3], [JM]. The basic object that they considered is the KP hierarchy of partial differential equations, which they study through a sequence of equivalent formulations that we describe below. The first formulation is a deformation (or Lax) equation of a formal pseudo-differential operator \(L = \partial + {{u}_{1}}{{\partial }^{{ - 1}}} + {{u}_{2}}{{\partial }^{{ - 2}}} + \ldots\) introduced in [S] and [W1]:
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Kac, V.G., van de Leur, J.W. (1993). The n-Component KP Hierarchy and Representation Theory. In: Fokas, A.S., Zakharov, V.E. (eds) Important Developments in Soliton Theory. Springer Series in Nonlinear Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58045-1_15
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