The CR problem and Hurwitz pairs applied to field theory and solid state physics (Q1185212)

The authors give explicit solutions for higher dimensional nonlinear Sigma models, as a sequel to their investigation of Hurwitz pairs. The paper starts with reviewing basic facts concerning the weighted Hurwitz pairs, the corresponding supercomplex structures, and the generalized Cauchy-Riemann problem. They consider the Fueter operators as an intrinsic version of Dirac-like operator. Next, the Hermitian pre-Hurwitz pairs are used to construct explicit solutions of higher-dimensional nonlinear Sigma models with values on complex Grassmannian manifolds. They obtain new results in the noncompact case. As application of the method, they study the soliton double sine-Gordon equation for ferroelectric crystals in the Finsler geometry and the soliton equation \(U_ tU_ x=2U_{tx}\tan{1\over 2}U\).