Solitary waves with intensity-dependent dispersion: variational characterization
Pattern Formation and Solitons
2021-10-27 v1
Abstract
A continuous family of singular solitary waves exists in a prototypical system with intensity-dependent dispersion. The family has a cusped soliton as the limiting lowest energy state and is formed by the solitary waves with bell-shaped heads of different lengths. We show that this family can be obtained variationally by minimization of mass at fixed energy and fixed length of the bell-shaped head. We develop a weak formulation for the singular solitary waves and prove that they are stable under perturbations which do not change the length of the bell-shaped head. Numerical simulations confirm the stability of the singular solitary waves.
Cite
@article{arxiv.2106.05413,
title = {Solitary waves with intensity-dependent dispersion: variational characterization},
author = {D. E. Pelinovsky and R. M. Ross and P. G. Kevrekidis},
journal= {arXiv preprint arXiv:2106.05413},
year = {2021}
}
Comments
15 pages, 7 figures