On integrability of tri-vector deformed sigma models

The integrability of different physical systems is an important property, since for classical systems one can construct a set of integrals of motion, and for quantum systems one can find a spectrum. The Lax-Zakharov-Shabat formalism is used to analyze classical field systems, such as two-dimensional sigma models.
I will discuss another approach to studying integrability of classical systems, based on methods of dynamical systems theory. In particular, I will show how such a method, based on knowledge of the phase space of the system, can be used to study a certain class of string solutions on various deformed backgrounds solving the 10-dimensional supergravity equations.