Results 1 
3 of
3
LOOP GROUP DECOMPOSITIONS IN ALMOST SPLIT REAL FORMS AND APPLICATIONS TO SOLITON THEORY AND GEOMETRY
, 805
"... Abstract. We prove a global Birkhoff decomposition for almost split real forms of loop groups, when an underlying finite dimensional Lie group is compact. Among applications, this shows that the dressing action by the whole subgroup of loops which extend holomorphically to the exterior discon the ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We prove a global Birkhoff decomposition for almost split real forms of loop groups, when an underlying finite dimensional Lie group is compact. Among applications, this shows that the dressing action by the whole subgroup of loops which extend holomorphically to the exterior discon the Uhierarchy of the ZSAKNS systems, on curved flats and on various other integrable systems, is global for compact cases. It also implies a global infinite dimensional Weierstrasstype representation for Lorentzian harmonic maps (1 + 1 wave maps) from surfaces into compact symmetric spaces. An “Iwasawatype ” decomposition of the same type of real form, with respect to a fixed point subgroup of an involution of the second kind, is also proved, and an application given. 1.
1 BianchiBäcklund transforms and dressing actions, revisited
, 808
"... The BianchiBäcklund transforms, which were introduced by Bianchi [2] for surfaces of positive constant Gauss curvature (equivalently, solutions of sinhGordon equation), are an extension of the Bäcklund transforms [7] for surfaces of negative constant Gauss curvature (equivalently, solutions of sin ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
The BianchiBäcklund transforms, which were introduced by Bianchi [2] for surfaces of positive constant Gauss curvature (equivalently, solutions of sinhGordon equation), are an extension of the Bäcklund transforms [7] for surfaces of negative constant Gauss curvature (equivalently, solutions of sineGordon equation). In contrast to the negative case, a