Three Series of Invariant Manifolds of the Sawada–Kotera Equation

We find a new infinite sequence of invariant manifolds for the Sawada–Kotera equation, in addition to the known two sequences of its symmetries and conservation laws. The elements of these three sequences are related cyclically by recursion relations similar to the Lenard formula for the KdV equation. For any $n>0$, there are two invariant manifolds of order $2n$, which allows one to construct two $n$-soliton solutions of the Sawada–Kotera equation.