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Updated: Aug 20, 2026

Spatial Separation of Molecular Conformers and Clusters
Published on: January 9, 2014
Beam stabilization in the two-dimensional nonlinear Schrödinger equation with an attractive potential by beam
Brenton John leMesurier1, Peter Leth Christiansen, Yuri B Gaididei
1Department of Mathematics, College of Charleston, Charleston, South Carolina 29424, USA. lemesurierb@cofc.edu
Abstract:
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrödinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrödinger equation in the critical dimension 2 and can lead to a stable oscillating beam. This is observed to involve a splitting of the beam into an inner part that is oscillatory and of subcritical power and an outer dispersing part. An analysis is given in terms of the rate competition between the linear and nonlinear focusing effects, radiation losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials.
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