Bifurcations and travelling wave solutions of a (2+1)-dimensional nonlinear Schrödinger equation

Wang, Juan; Chen, Longwei; Liu, Changfu

doi:10.1016/j.amc.2014.10.025

Cited by 8 publications

(4 citation statements)

References 10 publications

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“…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: 93%

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: 93%

Optical Bullets and Their Modulational Instability Analysis

Al-Ghafri¹,

Krishnan

Khan

et al. 2022

Applied Sciences

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“…The bifurcations and travelling wave solutions of the equation (1.1) are also studied by Wang [28]. Moreover, the general periodic solutions and RW solutions of the (2+1)dimensional NLS equation with the self-induced PT symmetric potential are derived [29].…”

Section: Introductionmentioning

confidence: 99%

High-order rational solutions and rogue wave for the (2 + 1)-dimensional nonlinear Schrödinger equation

Liu

Zhang

2020

Phys. Scr.

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In this paper, some exact explicit rational solutions of the (2 + 1)-dimensional nonlinear Schrödinger equation are presented in terms of the Gram determinants by using the bilinear method. The expressions of the fundamental line rogue wave, second-order parallel line rogue wave and third-order parallel line rogue wave all involve determinants whose matrix elements are simple polynomials. These line rogue waves, which all generate from a constant background with line contours and then disappear into the same background, are plotted in the (x, y)-plane. Moreover, we also consider different structures of higher-order rogue waves, and their dynamical behaviors are illustrated in the (x, t)-plane.

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“…In [21], the authors constructed the possible explicit parametric representations of the bounded travelling wave solutions and all kinds of phase portraits in the parametric space of Eq. (4) by using the approach of dynamical systems and the theory of bifurcations.…”

Section: Introductionmentioning

confidence: 99%

Optical soliton solutions to a (2+1) dimensional Schrödinger equation using a couple of integration architectures

Çankal

Yaşar

2020

Applied Mathematics and Nonlinear Sciences

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In this work, we consider a (2+1) dimensional nonlinear Schrödinger system which appears in the theory of nonlinear optics and describe transmission of the optical pulses in optical fibers. We attain certain special type traveling wave solutions of the under investigated model by help of finite series expansion and auxiliary differential equations. In this manner, we exploit exp(−ϕ(ε)) and modified Kudryashov approaches as solution procedures. Moreover, we make tanh ansatz because of the being even order of the reduced ordinary differential equation. The obtained solutions are in the form of dark soliton, combined soliton, symmetrical Lucas sine, Lucas cosine functions, and periodic wave solutions. We present also some graphical simulations of the solutions corresponding to values of parameters which leads to a better understanding the phenomena.

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Bifurcations and travelling wave solutions of a (2+1)-dimensional nonlinear Schrödinger equation

Cited by 8 publications

References 10 publications

Optical Bullets and Their Modulational Instability Analysis

Optical Bullets and Their Modulational Instability Analysis

High-order rational solutions and rogue wave for the (2 + 1)-dimensional nonlinear Schrödinger equation

Optical soliton solutions to a (2+1) dimensional Schrödinger equation using a couple of integration architectures

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