2+1-Dimensional Nonlinear Integrable Systems of Loewner-Type

摘要

A wide class of (2+1)-dimensional nonlinear systems integrable by the inversespectral transform method is presented. These are matrix generalizations on a nonlinear system originally introduced in a gas dynamic context by Loewner in 1952. The class of system investigated includes (2+1)-dimensional integrable generalizations of the chiral fields model equation, the non abelian sine Gordon equation, the Toda lattice equation as well as (2+1)-dimensional integrable systems on Grassmannian manifolds, including equations on CP(exp n) and RP(exp n). Certain (2+1)-dimensional integrable generalizations of the sine Gordon equation, invariant under rotation in the plane, are among the system considered.