Formal Series Symmetry Research Articles

Infinitely many symmetries of the Davey-Stewartson equation

Using a formal series symmetry method for the Davey-Stewartson equation (DSE), we find that there exist two sets of infinitely many formal series symmetries of the DSE. However, different from the Kadomtsev-Petviashvili equation (KPE), we failed to get infinitely many truncated symmetries. Only six truncated symmetries can be obtained simply from the formal series symmetries.

SYMMETRY STRUCTURE OF 2+1 DIMENSIONAL BILINEAR SAWADA-KOTERA EQUATION

We established a formal series symmetry theory for a type of generalized 2+1 dimensional bilinear equation in two different ways. Starting from a known time in-dependent symmetry or an arbitrary function of 1-D space, we can get a formal series symmetry with an arbitrary function of time t. For the 2+1 dimensional bilinear Sawada-Kotera equation, there exist six truncated symmetries. These truncated symmetries constitute an infinite dimensional Lie algebra. Some significant subalge-bras such as the Virasoro algebras are also given.