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- W1621106789 abstract "AbstractWe consider several integrable systems from a standpoint of the SL(2,R) invari-ant gauge theory. In the Drinfeld-Sokorov gauge, we get a one parameter familyof nonlinear equations from zero curvature conditions. For each value of the pa-rameter the equation is described by weak Lax equations. It is transformed to aset of coupled equations which pass the Painlev´e test and are integrable for anyinteger values of the parameter. Performing successive gauge transformations (theMiura transformations) on the system of equations we obtain a series of nonlinearequations.Keywords : Integrable system, Gauge transformation, weak Lax equation 1 Introduction Integrable systems in (1+1) dimensions have been discussed extensively so far andvarious techniques to analyze the integrability have been developed using the Lax pairs,the inverse scattering method, the Hirota’s direct method and the Painlev´e test etc.[1].However, these methods are mainly restricted in (1+1) dimensions. In (1+1) and higherdimensions, there is a well known conjecture by Ward [2] that any integrable systemsare derived from (anti) self-dual Yang-Mills gauge theories. So it is very important tore-examine integrable systems from gauge theoretical view points. The term gauge hasbeen often used with several different meanings in different papers and textbooks in the1" @default.
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- W1621106789 date "2001-08-24" @default.
- W1621106789 modified "2023-09-27" @default.
- W1621106789 title "Gauge Transformations and Weak Lax Equation" @default.
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