Symmetry in Nonlinear Partial Differential Equations and Rogue Waves

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 August 2024 | Viewed by 1520

Special Issue Editors


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Department of Mathematics, Sungkyunkwan University, Suwon 16419, Gyeonggi-do, Korea
Interests: nonlinear wave phenomena; partial differential equations; soliton theory; mathematics education
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Dipartimento di Matematica, Universita' degli Studi di Bologna, P.zza di Porta S. Donato, 540126 Bologna, Italy
Interests: mathematics
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Special Issue Information

Dear Colleagues,

Study of rogue waves has assisted many people not only to better understand natural phenomena but also to progress in the knowledge of nonlinear waves in general. The nonlinear Schrödinger (NLS) equation and its exact analytical solutions have been used as a mathematical model and for prototypes of rogue waves, also known as freak or extreme waves. Although the family of solitons on nonvanishing backgrounds was discovered in the 1970s and 1980s, it was not until the 2010s that experimental observations confirmed those theoretical predictions. In this Special Issue of Symmetry, we seek contributions from researchers on the topic of Symmetry in Rogue Waves. All types of contribution are welcome, including modeling, mathematical, physical, numerical, statistical, and experimental.

Dr. Natanael Karjanto
Prof. Angelo Favini
Guest Editors

Manuscript Submission Information

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Keywords

  • nonlinear waves
  • coherent structures
  • the nonlinear Schrödinger (NLS) equation
  • soliton on constant background
  • breathers
  • freak waves
  • rogue waves
  • extreme waves
  • wave packets
  • modulational instability
  • phase singularity
  • wavefront dislocation
  • variational formulation
  • maximum temporal amplitude
  • amplification factor
  • dissipation
  • surface gravity waves
  • nonlinear optics
  • superconductivity
  • plasma physics
  • Bose–Einstein condensates

Published Papers (1 paper)

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Research

18 pages, 340 KiB  
Article
New Hermite–Hadamard Type Inequalities in Connection with Interval-Valued Generalized Harmonically (h1,h2)-Godunova–Levin Functions
by Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Donal O’Regan, Muhammad Tariq and Kamsing Nonlaopon
Symmetry 2022, 14(10), 1964; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14101964 - 20 Sep 2022
Cited by 2 | Viewed by 868
Abstract
As is known, integral inequalities related to convexity have a close relationship with symmetry. In this paper, we introduce a new notion of interval-valued harmonically m,h1,h2-Godunova–Levin functions, and we establish some new Hermite–Hadamard inequalities. Moreover, we [...] Read more.
As is known, integral inequalities related to convexity have a close relationship with symmetry. In this paper, we introduce a new notion of interval-valued harmonically m,h1,h2-Godunova–Levin functions, and we establish some new Hermite–Hadamard inequalities. Moreover, we show how this new notion of interval-valued convexity has a close relationship with many existing definitions in the literature. As a result, our theory generalizes many published results. Several interesting examples are provided to illustrate our results. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Partial Differential Equations and Rogue Waves)
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