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 (Cabrera-Carnero I 2005 J. High Energy Phys. 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 also be constructed by means of the noncommutative extension of the uniton method proposed in (Lee K-M 2004 J. High Energy Phys. JHEP08(2004)054) by Lee. Particularly some specific solutions of the nc Liouville model are explicitly constructed.
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