Some Examples of the Twistor Construction

1986 ◽  
pp. 51-67 ◽  
Author(s):  
D. Burns
Keyword(s):  
Twistor Construction

scholarly journals INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT

1995 ◽  
Vol 07 (05) ◽  
pp. 743-808 ◽  
Author(s):  
KANEHISA TAKASAKI ◽  
TAKASHI TAKEBE
Keyword(s):  
Canonical Transformation ◽  
Toda Lattice ◽  
Integrable Hierarchies ◽  
General Solutions ◽  
Similar Construction ◽  
Toda Hierarchy ◽  
Technical Details ◽  
Dispersionless Limit ◽  
Toda Lattice Hierarchy ◽  
Twistor Construction

Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical transformation, quantization of which is dressing operators of the ordinary KP and Toda hierarchy. An alternative construction of general solutions of the ordinary KP and Toda hierarchy is given as twistor construction which is quantization of the similar construction of solutions of dispersionless hierarchies. These results as well as those obtained in previous papers are presented with proofs and necessary technical details.

scholarly journals Complex Multiplication in Twistor Spaces

2020 ◽  
Author(s):  
D Huybrechts
Keyword(s):  
Twistor Space ◽  
Complex Multiplication ◽  
K3 Surface ◽  
Twistor Spaces ◽  
Arithmetic Properties ◽  
Twistor Construction

Abstract Despite the transcendental nature of the twistor construction, the algebraic fibres of the twistor space of a K3 surface share certain arithmetic properties. We prove that for a polarised K3 surface with complex multiplication, all algebraic fibres of its twistor space away from the equator have complex multiplication as well.

On the Dispersionless Dym Hierarchy: Dressing Formulation and Twistor Construction

2003 ◽  
Vol 65 (2) ◽  
pp. 109-124 ◽  
Author(s):  
Yu-Tung Chen ◽  
Ming-Hsien Tu
Keyword(s):  
Twistor Construction

THE τ FUNCTIONS OF THE AKS HIERARCHY AND TWISTOR CORRESPONDENCE

1999 ◽  
Vol 11 (08) ◽  
pp. 981-999 ◽  
Author(s):  
PARTHA GUHA
Keyword(s):  
Gauge Group ◽  
Integrable Systems ◽  
Suitable Choice ◽  
Integrable Hierarchy ◽  
Geometrical Method ◽  
Soliton Equations ◽  
Yang Mills ◽  
Twistor Construction

Adler–Kostant–Symes scheme provides a geometrical method for constructing different integrable systems. We construct an AKS hierarchy and obtain the τ function solutions of this hierarchy. We also show that this AKS hierarchy is a reduction of self dual Yang–Mills (SDYM) equation hierarchy and discuss its twistor construction. Hence we re-establish once again that SDYM hierarchy is a universal integrable hierarchy, so that by appropriate reduction and suitable choice of gauge group this hierarchy produces all the well-known hierarchies of the soliton equations 1.

Sign in / Sign up

Export Citation Format

Share Document