scholarly journals An Elementary Introduction to Sato Theory

1988 ◽  
Vol 94 ◽  
pp. 210-241 ◽  
Author(s):  
Yasuhiro Ohta ◽  
Junkichi Satsuma ◽  
Daisuke Takahashi ◽  
Tetsuji Tokihiro
Keyword(s):  
Sato Theory

The q-deformed mKP hierarchy with two parameters

2018 ◽  
Vol 32 (16) ◽  
pp. 1850170
Author(s):  
Kelei Tian ◽  
Yanyan Ge ◽  
Xiaoming Zhu
Keyword(s):  
Additional Symmetry ◽  
Lax Equation ◽  
Quantum Calculus ◽  
Two Parameters ◽  
Sato Theory

In this paper, with the help of the biparametric quantum calculus we construct the Sato theory on the q-deformation modified Kadomtsev–Petviashvili hierarchy with two parameters (qp-mKP), which is a new deformation of classical mKP hierarchy. The Lax equation and dressing operator of qp-mKP hierarchy are derived. By considering the M operator and [Formula: see text] operator, the additional symmetry of qp-mKP hierarchy is obtained.

Symmetries, sato theory, and tau functions

1995 ◽  
Vol 56 (1-2) ◽  
pp. 147-164 ◽  
Author(s):  
Robert Carroll
Keyword(s):  
Tau Functions ◽  
Sato Theory

GAUGE TRANSFORMATIONS AND RECIPROCAL LINKS IN 2 + 1 DIMENSIONS

1993 ◽  
Vol 05 (02) ◽  
pp. 299-330 ◽  
Author(s):  
W. OEVEL ◽  
C. ROGERS
Keyword(s):  
Differential Operators ◽  
Bäcklund Transformations ◽  
Gauge Transformations ◽  
Pseudo Differential Operators ◽  
Backlund Transformations ◽  
Lax Equations ◽  
Sato Theory

Generalized Lax equations are considered in the spirit of Sato theory. Three decompositions of an underlying algebra of pseudo-differential operators lead, in turn, to three different classes of integrable nonlinear hierarchies. These are associated with Kadomtsev-Petviashvili, modified Kadomtsev-Petviashvili and Dym hierarchies in 2 + 1 dimensions. Miura- and auto-Bäcklund transformations are shown to originate naturally from gauge transformations of the Lax operators. General statements on reciprocal links between these hierarchies are established, which, in particular, give rise to novel reciprocal auto-Bäcklund transformations for the Dym hierarchy. These links are formulated as Darboux theorems for the associated Lax operators.

Eigenfunction equations in Sato theory

1990 ◽  
Vol 23 (12) ◽  
pp. L609-L612 ◽  
Author(s):  
B G Konopelchenko
Keyword(s):  
Sato Theory

Some General Formulas in the Sato Theory

2003 ◽  
Vol 72 (2) ◽  
pp. 448-449 ◽  
Author(s):  
Da-jun Zhang ◽  
Deng-yuan Chen
Keyword(s):  
Sato Theory
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