title: Soliton stability versus collapse
abstract: Nonlinear Schrodinger equations with positive potentials are investigated. Stability of their stationary ground states is confronted with properties of nonlinear blow-up. The stability condition for these soliton modes is shown to involve restrictions on the potential slope, which do not forbid the collapse. We prove that stable ground states must have a power integral below their counterpart with no potential.
authors.affiliation: Commissariat a l'Energie Atomique, CEA-DAM/Ile-de-France, B.P. 12, 91680 Bruyeres-le-Chainsertion marktel, France.
authors.initials: L
authors.lastname: Berge