Multi-solitons of one-dimensional Boussinesq equation
Analysis of PDEs
2024-06-26 v1
Abstract
The existence of multi-speed solitary waves for the one-dimensional good Boussinesq equation with a power nonlinearity is proven. These solutions are shown to behave at large times as a pair of scalar solitary waves traveling at different speeds. Both subcritical and supercritical cases are treated. The proof is based on the construction of approximations of the multi-speed solitary waves by solving an equivalent system backward in time and using energy methods to obtain uniform estimates.
Cite
@article{arxiv.2406.17498,
title = {Multi-solitons of one-dimensional Boussinesq equation},
author = {Vicente Alvarez and Amin Esfahani},
journal= {arXiv preprint arXiv:2406.17498},
year = {2024}
}