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Abstract Up to the third-order rogue wave solutions of the Sasa–Satsuma (SS) equation are derived based on the Hirota’s bilinear method and Kadomtsev–Petviashvili hierarchy reduction method. They are expressed explicitly by rational functions with both the numerator and denominator being the determinants of even order. Four types of intrinsic structures are recognized according to the number of zero-amplitude points. The first- and second-order rogue wave solutions agree with the solutions obtained so far by the Darboux transformation. In spite of the very complicated solution form compared with the ones of many other integrable equations, the third-order rogue waves exhibit two configurations: either a triangle or a distorted pentagon. Both the types and configurations of the third-order rogue waves are determined by different choices of free parameters. As the nonlinear Schrödinger equation is a limiting case of the SS equation, it is shown that the degeneration of the first-order rogue wave of the SS equation converges to the Peregrine soliton.
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This content will become publicly available on November 13, 2026
General rogue waves of infinite order: exact properties, asymptotic behaviour, and effective numerical computation
This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schrödinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit processes involving large-amplitude waves, and they have also appeared in some physical models not directly connected with nonlinear Schrödinger equations. We establish the following key property of these solutions: they are all in $$L^2(\mathbb{R})$$ with respect to the spatial variable but they exhibit anomalously slow temporal decay. In this paper, we define general rogue waves of infinite order, establish their basic exact and asymptotic properties, and provide computational tools for calculating them accurately.
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- PAR ID:
- 10650352
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Nonlinear Waves
- Volume:
- 1
- ISSN:
- 3033-4268
- Subject(s) / Keyword(s):
- long-time behavior of solutions nonlinear Schrödinger equation Riemann-Hilbert problems
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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