Complex KdV rogue waves from gauge-Miura transformation

Author:

Ysla F. Adans, Guilherme França, José F. Gomes, Gabriel V. Lobo, Abraham H. Zimerman

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), High Energy Physics - Theory (hep-th), Mathematical Physics (math-ph), Pattern Formation and Solitons (nlin.PS)

journal:

J. Phys.: Conf. Ser. 2667 (2023) 012027

date:

2023-12-21 00:00:00

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.

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