Generalized perturbation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mi>M</mml:mi><mml:mo>)</mml:mo></mml:math>-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation

Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya

doi:10.1103/physreve.92.012917

Cited by 110 publications

(39 citation statements)

References 48 publications

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“…Possibilities to test the theoretical results are also discussed. The results here can be extended to a three-wave resonant system [15,58], scalar NLSE with high-order effects [59][60][61], and other nonlinear systems [62][63][64][65][66][67][68].…”

Section: Discussionmentioning

confidence: 84%

Generation mechanisms of fundamental rogue wave spatial-temporal structure

et al. 2017

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We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation. Furthermore, our results show that N-component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

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Section: Discussionmentioning

confidence: 84%

Generation mechanisms of fundamental rogue wave spatial-temporal structure

et al. 2017

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“…Due to the reduction condition (37), t a becomes a dummy variable which can be taken as zero. Thusm (N−i,N− j,n) 2i−1,2 j−1 p=ζ,q=ζ * andτ n reduce to m (N−i,N− j,n) 2i−1,2 j−1 and τ n (29) in Lemma 2.2.…”

Section: Algebraic Solutions For the (1+1)-dimensional Yo Systemmentioning

confidence: 99%

General High-order Rogue Waves of the (1+1)-Dimensional Yajima–Oikawa System

Chen

Feng

et al. 2018

J. Phys. Soc. Jpn.

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General high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa (YO) system are derived by using Hirota's bilinear method and the KP-hierarchy reduction technique. These rogue wave solutions are presented in terms of determinants in which the elements are algebraic expressions. The dynamics of first and higher-order rogue wave are investigated in details for different values of the free parameters. It is shown that the fundamental (first-order) rogue waves can be classified into three different patterns: bright, intermediate and dark ones. The high-order rogue waves correspond to the superposition of fundamental rogue waves. Especially, compared with the nonlinear Schödinger equation, there exists an essential parameter α to control the pattern of rogue wave for both first-and high-order rogue waves since the YO system does not possess the Galilean invariance.

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“…Section 4 is devoted to a discrete version of the generalised perturbation (n, N − n)-fold Darboux transformation of Eq. (1.1), used to study integrable continuous NPDEs [41,42,44,45] and the discrete coupled Ablowitz-Ladik equation [43]. These ideas are applied to Eq.…”

Section: Introductionmentioning

confidence: 99%

Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations

Wen¹

2018

EAJAM

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The generalised perturbation (n, N − n)-fold Darboux transformation is used to derive new higher-order rogue wave and rational soliton solutions of the discrete complex mKdV equations. The structure of such waves and details of their evolution are investigated via numerical simulations, showing that the strong interaction yields weak oscillation and stability whereas the weak interaction is associated with strong oscillation and instability. A small noise has a weak influence on the wave propagation for the strong interaction, but substantially changes the wave behaviour in the weak interaction case.

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Generalized perturbation(n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation

Cited by 110 publications

References 48 publications

Generation mechanisms of fundamental rogue wave spatial-temporal structure

Generation mechanisms of fundamental rogue wave spatial-temporal structure

General High-order Rogue Waves of the (1+1)-Dimensional Yajima–Oikawa System

Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations

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