About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane

Abstract

The relation of the noncommutative self-dual Chern-Simons (NCSDCS) system to the noncommutative generalizations of Toda and of affine Toda field theories is investigated more deeply. This paper continues the programme initiated in $JHEP10(2005)071$, where it was presented how it is possible to define Toda field theories through second order differential equation systems starting from the NCSDCS system. Here we show that using the connection of the NCSDCS to the noncommutative chiral model, exact solutions of the Toda field theories can be also constructed by means of the noncommutative extension of the uniton method proposed in $JHEP0408(2004)054$ by Ki-Myeong Lee. Particularly some specific solutions of the nc Liouville model are explicit constructed.

24 pages

References in corpus (7)

• Integrable Noncommutative Sine-Gordon Model
• Explorations of the Extended ncKP Hierarchy
• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Bosonized noncommutative bi-fundamental fermion and S-duality
• Consistent Interactions of the 2+1 Dimensional Noncommutative Chern-Simons Field
• Non-commutative solitons and strong-weak duality
• Abelian Toda field theories on the noncommutative plane

Cited by in corpus (2)

• Noncommutative Ward's Conjecture and Integrable Systems
• Perturbed nonlinear models from Noncommutativity