New integrable sectors in the Skyrme and four-dimensional CPn models

The application of a weak integrability concept to the Skyrme and CPn models in four dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic configurations, is derived. This procedure can be applied to the massive Skyrme model as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge is given. In the case of CPn models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.