On separability of non-linear Schrodinger operators with matrix potentials.

In this paper, we studied the separability of the non-linear Schrodinger operator of the form S u x = − Δ u x + V x , u u x , where Δ u x = ∑ i = 1 n ∂ 2 u x ∂ x i 2 , with the non-linear matrix potential V x , u . We obtained the sufficient conditions for separability of this operator in the space L 2 R n ℓ and we established the suitable coercive inequalities. [ABSTRACT FROM AUTHOR]