Nonlinear systems with exponential interaction that are generated by Kählerian chiral models

The Pohlmeyer transformation relating the $O(3)$-$\sigma$-model and the sine-Gordon equation is generalized to the case of a Kählerian chiral model. The transformation leads to matrix systems of the form $B^{i}_{z\bar{z}}+C^{ij}\exp B^{j}+D^i=0$ (where $C^ij$ are not Cartan matrices with the exception of one of the two-dimensional Cartan matrices of the Kac–Moody algebra) which have solutions obtained from the original chiral model (instantons, merons, complete solutions with finite action of the $CP^{n}$ and $O(2k+1)$-models). The construction also leads to the sh-Gordon and Doddl–Bullough equations.