Complex KdV rogue waves from gauge-Miura transformation
Exactly Solvable and Integrable Systems
2023-12-22 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Pattern Formation and Solitons
Abstract
The gauge-Miura correspondence establishes a map between the entire KdV and mKdV hierarchies, including positive and also negative flows, from which new relations besides the standard Miura transformation arise. We use this correspondence to classify solutions of the KdV hierarchy in terms of elementary tau functions of the mKdV hierarchy under both zero and nonzero vacua. We illustrate how interesting nonlinear phenomena can be described analytically from this construction, such as ``rogue waves'' of a complex KdV system that corresponds to a limit of a vector nonlinear Schr\"odinger equation.
Keywords
Cite
@article{arxiv.2312.14101,
title = {Complex KdV rogue waves from gauge-Miura transformation},
author = {Ysla F. Adans and Guilherme França and José F. Gomes and Gabriel V. Lobo and Abraham H. Zimerman},
journal= {arXiv preprint arXiv:2312.14101},
year = {2023}
}
Comments
8 pages. Int. Symp. Quantum Theory and Symmetries (QST12)