Transformation Groups for Soliton Equations – Euclidean Lie Algebras and Reduction of the KP Hierarchy – | Zendy

Etsurō Date | Zendy; Michio Jimbo | Zendy; Masaki Kashiwara | Zendy; Tetsuji Miwa | Zendy

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Transformation Groups for Soliton Equations – Euclidean Lie Algebras and Reduction of the KP Hierarchy –

Author(s) -

Etsurō Date,

Michio Jimbo,

Masaki Kashiwara,

Tetsuji Miwa

Publication year - 1982

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195183297

Subject(s) - mathematics , korteweg–de vries equation , pure mathematics , hierarchy , lie algebra , soliton , subalgebra , transformation (genetics) , kdv hierarchy , sine gordon equation , algebra over a field , kadomtsev–petviashvili equation , reduction (mathematics) , partial differential equation , mathematical analysis , nonlinear system , burgers' equation , geometry , physics , biochemistry , chemistry , quantum mechanics , economics , market economy , gene

This is the last chapter of our series of papers [1], [3], [10], [11] on transformation groups for soliton equations. In [1] a link between the KdV (Korteweg de Vries) equation and the affine Lie algebra A[^ was found: the vertex operator that affords an explicit realization of the basic representation of A{ [2] acts infinitesimally on the i functions of the KdV hierarchy. It was shown also that this link between the KdV equation and A[ comes from a similar link between the KP (Kadomtsev-Petviashvili) equation and gl(oo); the restriction to the subalgebra A{^ in gl(oo) reduces the KP hierarchy to the KdV hierarchy.

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