Solitary Wave Dynamics in an External Potential

By J. Fröhlich, Stephen Gustafson, B. L. G. Jonsson, B. Jonsson, I. Sigal. 2003

174 citations recorded by the source corpus.

We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing inertial motions of stable solitary waves. We consider solutions of the equations with a non-vanishing external potential corresponding to initial conditions close to one of these solitary wave solutions and show that, over a large interval of time, they describe a solitary wave whose center of mass motion is a solution of Newton’s equations of motion for a point particle in the given external potential, up to small corrections corresponding to radiation damping.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bc99b84b7ef2174b9aeae34f283643a1d9612a2c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Uniqueness of ground states for pseudorelativistic Hartree equations (2008, background): “As mentioned before, this spectral result is of independent interest, since it proves a key assumption in [Fröhlich et al. 2002; Fröhlich et al. 2004; Jonsson et al. 2006; Abou Salem 2007].”
Fast Soliton Scattering by Delta Impurities (2006, result): “In the mathematical literature the dynamics of solitons in the presence of external potentials has been studied in high velocity or semiclassical limits following the work of Floer and Weinstein [6], and Bronski and Jerrard [1] – see [7] for recent results and a review of the subject.”