2013/12/15 by David I. Ketcheson, Ketcheson, David I., Manuel Quezada de Luna +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #nlin.PS
paper · pdf · doi:10.48550/arxiv.1312.4122
arxiv created 2013/12/15 · openalex publication_date 2013/12/15 · arxiv updated 2013/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the sound speed of the medium. A high-order homogenized model confirms this effective dispersive behavior and its solutions agree well with those obtained by direct simulation of the variable-coefficient system. These waves are observed to be long-time stable, globally attracting solutions that arise in general as solutions to nonlinear wave problems with periodically-varying sound speed. They share some properties with known classes of solitary waves, but possess important differences as well.