Principal models on a solvable group with nonconstant metric
  Field equations for generalized principle models with nonconstant metric are derived and ansatz for their Lax pairs is given. Equations that define the Lax pairs are solved for the simplest solvable group. The solution is dependent on one free variable that can serve as the spectral parameter. Painleve analysis of the resulting model is performed and its particular solutions are found 
L. Hlavaty