New maximal dimension of invariant subspaces to coupled systems with two-component equations

• A new extension of the theorem “on maximal dimension” to the vector operators under certain conditions is given.
• Several concrete examples are presented to illustrate this result.
• The complete classification of the Torrisi’s system is obtained.

In this paper, new maximal dimension of invariant subspaces to coupled systems with two-component equations is estimated under certain conditions. It is shown that if the really coupled operator F=(F1,F2)F=(F1,F2) with orders {k1,k2}(k1⩾k2){k1,k2}(k1⩾k2) preserves the invariant subspace Wn11×Wn22(0