Complex KdV rogue waves from gauge-Miura transformation

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...

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Published inJournal of physics. Conference series Vol. 2667; no. 1; pp. 12027 - 12034
Main Authors Adans, Ysla F., França, Guilherme, Gomes, José F., Lobo, Gabriel V., Zimerman, Abraham H.
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.12.2023
Subjects
Hierarchies
Mathematical analysis
Nonlinear phenomena
Physics
Schrodinger equation
Transformations (mathematics)
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Summary: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 Schrödinger equation.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/2667/1/012027