Symmetry approach to integrability and non-associative algebraic structures

The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand side are considered. Such systems are associated with associative algebras and, more generally, with non-associative algebraic structures, whose structural constants are defined by the coefficients of the system under consideration. We explore which structures correspond to polynomial integrable models. Integrable systems polynomial in derivatives are described in geometric terms. The third part we consider integrable vector izotropic and anizotropic systems.