Novel high‐order breathers and rogue waves in the Boussinesq equation via determinants
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6148
Abstract: By virtue of the bilinear method and the Kadomtsev–Petviashvili (KP) hierarchy reduction technique, wider classes of high‐order breather and semirational and rogue wave solutions to the Boussinesq equation are derived. These solutions are presented explicitly… read more here.
Keywords: rogue; rogue wave; equation; rogue waves ... See more keywords
Rogue wave-type solutions of the mKdV equation and their relation to known NLSE rogue wave solutions
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-017-3991-2
Abstract: We present the first four exact rational solutions of the set of rational solutions of the modified Korteweg–de Vries equation. These solutions can be considered as rogue waves of the corresponding equation. Comparison with rogue… read more here.
Keywords: rogue; wave solutions; type solutions; wave type ... See more keywords
Generalized Darboux transformation and parameter-dependent rogue wave solutions to a nonlinear Schrödinger system
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-018-4198-x
Abstract: In this work, we are concerned with a generalized nonlinear Schrödinger equation, which can describe the propagation of nonlinear wave phenomena in plasma, optics and in deep water field. We construct, up to the second-order… read more here.
Keywords: rogue; generalized darboux; nonlinear schr; wave solutions ... See more keywords
Integral relations for rogue wave formations of Gardner equation
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DOI: 10.1007/s11071-019-05377-9
Abstract: Rogue wave structures can often be described by a set of rational solutions. These can be derived for physical systems satisfying various well-known nonlinear equations. We present integral relations which characterize the Gardner rogue waves,… read more here.
Keywords: relations rogue; integral relations; rogue wave; formations gardner ... See more keywords
Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity
Sign Up to like & getrecommendations! Published in 2022 at "Optical and Quantum Electronics"
DOI: 10.1007/s11082-022-03606-x
Abstract: This article retrieve lump, lump with one kink and rogue wave soliton for the time fractional resonant nonlinear Schrödinger equation with parabolic law having weak nonlocal nonlinearity. According to theory of dynamical systems, Schrödinger equation… read more here.
Keywords: fractional resonant; rogue wave; time fractional; dinger equation ... See more keywords
General lump solutions, lumpoff solutions, and rogue wave solutions with predictability for the (2+1)-dimensional Korteweg-de Vries equation
Sign Up to like & getrecommendations! Published in 2019 at "Computational and Applied Mathematics"
DOI: 10.1007/s40314-019-0938-x
Abstract: In this work, the (2+1)-dimensional Korteweg-de Vries equation is investigated, which can be used to represent the amplitude of the shallow–water waves in fluids or electrostatic wave potential in plasmas. By employing the properties of… read more here.
Keywords: lumpoff solutions; dimensional korteweg; korteweg vries; vries equation ... See more keywords
A study of lump and line rogue wave solutions to a (2+1)-dimensional nonlinear equation
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2021.104274
Abstract: Abstract In this article, a new (2+1)-dimensional extension of the Hietarinta equation is proposed. Two classes of lump and line rogue wave solutions are obtained for this equation by means of the Hirota bilinear method.… read more here.
Keywords: line rogue; rogue wave; lump line; wave solutions ... See more keywords
Rogue wave, interaction solutions to the KMM system
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Magnetism and Magnetic Materials"
DOI: 10.1016/j.jmmm.2020.166590
Abstract: Abstract In this paper, the consistent tanh expansion (CTE) method and the truncated Painleve analysis are applied to the Kraenkel-Manna-Merle (KMM) system, which describes propagation of short wave in ferromagnets. Two series of analytic solutions… read more here.
Keywords: kmm system; rogue wave; system; interaction solutions ... See more keywords
Characterization of optical rogue wave based on solitons' eigenvalues of the integrable higher-order nonlinear Schrödinger equation
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DOI: 10.1016/j.optcom.2016.08.048
Abstract: Abstract The dynamics of the optical rogue wave phenomenon in the framework of integrable higher-order nonlinear Schrodinger equation (HNLSE) including the third order dispersion term is presented in this paper. When rogue waves generate through… read more here.
Keywords: rogue; order; optical rogue; integrable higher ... See more keywords
Generation mechanism and prediction of an observed extreme rogue wave
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DOI: 10.1038/s41598-022-05671-4
Abstract: Rogue waves are individual ocean surface waves with crest height \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta$$\end{document}η or trough-to-crest height H that are large compared to the significant wave height \documentclass[12pt]{minimal} \usepackage{amsmath}… read more here.
Keywords: usepackage; rogue; document; documentclass 12pt ... See more keywords
Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions.
Sign Up to like & getrecommendations! Published in 2018 at "Chaos"
DOI: 10.1063/1.5019754
Abstract: A study of rogue-wave solutions in the reverse-time nonlocal nonlinear Schrödinger (NLS) and nonlocal Davey-Stewartson (DS) equations is presented. By using Darboux transformation (DT) method, several types of rogue-wave solutions are constructed. Dynamics of these… read more here.
Keywords: nonlocal nonlinear; wave solutions; reverse time; time ... See more keywords