Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations
Analysis of PDEs
2025-11-19 v1
Abstract
Given a nonlinear dispersive equation which admits a scaling invariance, there may exist self-similar solutions. In this work, we present a systematic approach for the construction of small-amplitude self-similar solutions, together with precise asymptotic descriptions at both small and large frequency scales. These ideas are then applied to three classic dispersive models: the modified Benjamin-Ono, the quartic Korteweg-de Vries and the cubic nonlinear Schr\"odinger equations.
Cite
@article{arxiv.2511.14586,
title = {Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations},
author = {Simão Correia and Gonçalo Pereira and Thyago S. R. Santos},
journal= {arXiv preprint arXiv:2511.14586},
year = {2025}
}
Comments
44 pages