On Some Classes of mKdV Periodic Solutions
Pattern Formation and Solitons
2009-11-10 v1
Abstract
We obtain exact periodic solutions of the positive and negative modified Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices through direct numerical simulations. While the positive mKdV breather lattice solutions are found to be unstable, the two-soliton lattice solution of the same equation is found to be stable. Similarly, a negative mKdV lattice solution is found to be stable. We also touch upon the implications of these results for the KdV equation.
Keywords
Cite
@article{arxiv.nlin/0410047,
title = {On Some Classes of mKdV Periodic Solutions},
author = {P. G. Kevrekidis and Avinash Khare and A. Saxena and G. Herring},
journal= {arXiv preprint arXiv:nlin/0410047},
year = {2009}
}
Comments
8 pages, 3 figures, to appear in J. Phys. A