title: Nonlocal solitons in the parametrically driven nonlinear Schrödinger equation: stability analysis.
abstract: We study analytically and numerically the linear stability of weakly nonlocal solitons in the parametrically driven nonlinear Schrödinger equation. Two exact solutions are derived in an implicit form. We show analytically that despite the well-known stabilizing properties of nonlocality one of the solitons remains unstable even in the nonlocal case for any values of the dissipation, the damping, and the degree of nonlocality. The second soliton, as compared to its local counterpart, attains wider stable regions in the space of the parameters of the system.
authors.affiliation: Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag Rondebosch 7701, South Africa. m.moltschan@gmail.com
authors.forename: Maxim A
authors.initials: MA
authors.lastname: Molchan