On separability of non-linear Schrodinger operators with matrix potentials

摘要

In this paper, we studied the separability of the non-linear Schrodinger operator of the form Su (x) = -Delta u (x) + V (x, u) u (x) , where Delta u (x) = Sigma(n )(i=1)partial derivative(2)u(x)/partial derivative 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.