Year: 2024
Type: article
Abstract: We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents α + 1 with 4 3 < α < 3 , we employ fixed-point arguments to find near-sonic solitary waves having scaled velocity profiles close to non-degenerate solitary-wave profiles of fractional KdV or generalized Benjamin–Ono equations. These equations were recently found to approximately govern unidirectional long-wave motions in these lattices.
Source: Nonlinearity
Authors: Benjamin Ingimarson, Robert L Pego
Institution: Carnegie Mellon University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,165
Funder: National Science Foundation
OpenAlex ID: W4404138544