Circular viewpoint of higher-order rogue wave structures of the nonlinear Schrödinger equation

A. Ankiewicz

doi:10.1088/1402-4896/adb79c

Circular viewpoint of higher-order rogue wave structures of the nonlinear Schrödinger equation

A. Ankiewicz^*

^*Corresponding author for this work

Department of Fundamental & Theoretical Physics

Research output: Contribution to journal › Article › peer-review

Abstract

We analyze rogue wave patterns for various orders of the nonlinear Schrödinger equation for large values of solution parameters. We use a combination of exact solutions, geometric constructions and polynomial approximations for analysis, and introduce a new way of viewing the formations of rogue waves, including the triangular ones, by showing that they all can be represented as occupying circular shells, some of which contain ‘nuclei’.

Original language	English
Article number	045204
Pages (from-to)	1-15
Number of pages	15
Journal	Physica Scripta
Volume	100
Issue number	4
DOIs	https://doi.org/10.1088/1402-4896/adb79c
Publication status	Published - 1 Apr 2025

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10.1088/1402-4896/adb79cLicence: CC BY

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title = "Circular viewpoint of higher-order rogue wave structures of the nonlinear Schr{\"o}dinger equation",

abstract = "We analyze rogue wave patterns for various orders of the nonlinear Schr{\"o}dinger equation for large values of solution parameters. We use a combination of exact solutions, geometric constructions and polynomial approximations for analysis, and introduce a new way of viewing the formations of rogue waves, including the triangular ones, by showing that they all can be represented as occupying circular shells, some of which contain {\textquoteleft}nuclei{\textquoteright}.",

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AB - We analyze rogue wave patterns for various orders of the nonlinear Schrödinger equation for large values of solution parameters. We use a combination of exact solutions, geometric constructions and polynomial approximations for analysis, and introduce a new way of viewing the formations of rogue waves, including the triangular ones, by showing that they all can be represented as occupying circular shells, some of which contain ‘nuclei’.

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KW - higher-order rogue waves

KW - nonlinear schrödinger equation

KW - nonlinear structures

UR - https://www.scopus.com/pages/publications/86000316821

U2 - 10.1088/1402-4896/adb79c

DO - 10.1088/1402-4896/adb79c

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JO - Physica Scripta

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Circular viewpoint of higher-order rogue wave structures of the nonlinear Schrödinger equation

Abstract

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