Rogue waves in the (2+1)-dimensional nonlinear Schrodinger equations

Liu, Changfu; Wang, Zeping; Dai, Zhengde; Chen, Longwei

doi:10.1108/hff-03-2013-0094

Cited by 9 publications

(4 citation statements)

References 25 publications

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“…The bilinear form of 2D-NLSS was derived by Radha and Lakshmanan [48] so as to obtain soliton solutions. Further to this, numerous authors have extracted breather and rogue wave solutions [49][50][51][52]. Additionally, optical wave solutions of different forms including bright soliton, dark soliton, periodic waves, and others have been found as well [53][54][55][56][57].…”

Section: Introductionmentioning

confidence: 92%

Optical Bullets and Their Modulational Instability Analysis

Al-Ghafri¹,

Krishnan

Khan

et al. 2022

Applied Sciences

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The current work is devoted to investigating the multidimensional solitons known as optical bullets in optical fiber media. The governing model is a (3+1)-dimensional nonlinear Schrödinger system (3D-NLSS). The study is based on deriving the traveling wave reduction from the 3D-NLSS that constructs an elliptic-like equation. The exact solutions of the latter equation are extracted with the aid of two analytic approaches, the projective Riccati equations and the Bernoulli differential equation. Upon applying both methods, a plethora of assorted solutions for the 3D-NLSS are created, which describe mixed optical solitons having the profiles of bright, dark, and singular solitons. Additionally, the employed techniques provide several kinds of periodic wave solutions. The physical structures of some of the derived solutions are depicted to interpret the nature of the medium characterized by the 3D-NLSS. In addition, the modulation instability of the discussed model is examined by making use of the linear stability analysis.

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Section: Introductionmentioning

confidence: 92%

Optical Bullets and Their Modulational Instability Analysis

Al-Ghafri¹,

Krishnan

Khan

et al. 2022

Applied Sciences

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“…Plenty of analytical solutions have also been discovered, including various solitons, [27][28][29][30] Jacobi elliptic function solutions, [31] and line rogue waves. [32][33][34][35][36] In Ref. [37] Radha and Lakshmanan generated a new class of "induced localized structures" by the line soliton's interaction with a curved soliton.…”

Section: Introductionmentioning

confidence: 99%

From breather solutions to lump solutions: A construction method for the Zakharov equation

Yuan 袁,

Ghanbari,

Zhang 张

et al. 2023

Chinese Phys. B

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Periodic solutions of the Zakharov equation are investigated in this paper. Through performing the limit operation $\lambda_{2l-1}\to\lambda_1$ on the eigenvalues of the Lax pair obtained from the $n$-fold Darboux transformation, an order-$n$ breather-positon solution is first obtained from a plane wave seed. It is then proven that an order-$n$ lump solution can be further constructed through taking the limit $\lambda_1\to\lambda_0$ on the breather-positon solution, because the unique eigenvalue $\lambda_0$ associated with the Lax pair eigenfunction $\Psi(\lambda_0)=0$ corresponds to the limit of the infinite-periodic solutions. A convenient procedure of generating higher-order lump solutions of the Zakharov equation is also investigated based on the idea of the degeneration of double eigenvalues in multi-breather solutions.

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“…With the in-depth study of the soliton problem, a large number of NLEEs with soliton solutions have appeared in many fields such as fluid physics, solid state physics, basic particle physics, laser, plasma physics, superconductivity physics, condensed matter physics and biophysics, etc. (Ebadi et al , 2015; Wazwaz, 2015; Triki and Wazwaz, 2016; Xu and Chen, 2015; Chen et al , 2015a; Liu et al , 2015; Kang et al , 2015; Chen et al , 2015b; Tian and Zhang, 2014, 2012; Xu et al , 2015; Tu et al , 2016c; Wang et al , 2016, 2017e).…”

Section: Introductionmentioning

confidence: 99%

Rogue waves, homoclinic breather waves and soliton waves for a (3 + 1)-dimensional non-integrable KdV-type equation

Mao

Tian

Zhang

2019

HFF

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PurposeThe purpose of this paper is to find the exact solutions of a (3 + 1)-dimensional non-integrable Korteweg-de Vries type (KdV-type) equation, which can be used to describe the stability of soliton in a nonlinear media with weak dispersion.Design/methodology/approachThe authors apply the extended Bell polynomial approach, Hirota’s bilinear method and the homoclinic test technique to find the rogue waves, homoclinic breather waves and soliton waves of the (3 + 1)-dimensional non-integrable KdV-type equation. The used approach formally derives the essential conditions for these solutions to exist.FindingsThe results show that the equation exists rogue waves, homoclinic breather waves and soliton waves. To better understand the dynamic behavior of these solutions, the authors analyze the propagation and interaction properties of the these solutions.Originality/valueThese results may help to investigate the local structure and the interaction of waves in KdV-type equations. It is hoped that the results can help enrich the dynamic behavior of such equations.

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Rogue waves in the (2+1)-dimensional nonlinear Schrodinger equations

Cited by 9 publications

References 25 publications

Optical Bullets and Their Modulational Instability Analysis

Optical Bullets and Their Modulational Instability Analysis

From breather solutions to lump solutions: A construction method for the Zakharov equation

Rogue waves, homoclinic breather waves and soliton waves for a (3 + 1)-dimensional non-integrable KdV-type equation

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