Lie algebraic structures of some (1+2)-dimensional Lax integrable systems

The paper proposes an approach to constructing the symmetries and their algebraic structures for isospectral and nonisospectral evolution equations of (1+2)-dimensional systems associated with the linear problem of Sato theory. To do that, we introduce the implicit representations of the isospectral flows {Km} and nonisospectral flows {σn} in the high dimensional cases. Three examples, the Kodomstev–Petviashvili system, BKP system and new CKP system, are considered to demonstrate our method.