On (2+1)-dimensional nonlinear systems of Loewner-type

Abstract A wide class of novel (2+1)-dimensional nonlinear systems is presented. These arise out of a reinterpretation of infinitesimal Backlund transformations originally introduced in a gas-dynamic context by Loewner in 1952. The class of systems investigated includes (2+1)-dimensional extensions of the chiral-field model equation, the non-Abelian sine-Gordon equation, the Toda lattice system as well as (2+1)-dimensional systems on Grassmannian manifolds. In particular, a (2+1)-dimensional generalisation of the sine-Gordon equation is presented in which the two spatial variables occur on an equal footing.