Submodels of Nonlinear Grassmann Sigma Models in Any Dimension and Conserved Currents, Exact Solutions

TL;DR

This paper extends the study of nonlinear Grassmann sigma models by constructing conserved currents and exact solutions, especially for ${f C}P^1$-models, and generalizes these to higher-order cases.

Contribution

It constructs almost all conserved currents for submodels and extends the equations and conserved currents to higher-order models.

Findings

Constructed almost all conserved currents for submodels.

Extended equations and conserved currents to higher-order models.

Reviewed and generalized the Smirnov and Sobolev construction.

Abstract

In the preceding paper(hep-th/9806084), we constructed submodels of nonlinear Grassmann sigma models in any dimension and, moreover, an infinite number of conserved currents and a wide class of exact solutions. In this paper, we first construct almost all conserved currents for the submodels and all ones for the one of ${\bf C}P^1$-model. We next review the Smirnov and Sobolev construction for the equations of ${\bf C}P^1$-submodel and extend the equations, the S-S construction and conserved currents to the higher order ones.