Optical dark and dark-singular soliton solutions of (1+2)-dimensional chiral nonlinear Schrodinger’s equation

Raza, Nauman; Javid, Ahmad

doi:10.1080/17455030.2018.1451009

Cited by 106 publications

(36 citation statements)

References 36 publications

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“…Exact solutions produce corporal information to describe the physical behavior of system connected with these NLEs. In recent years, several efficient methods including method of extended tanh [1,2], tanh-coth [3,4], Hirota's direct [5,6], sine-cosine [7,8], extended direct algebraic [9,10], extended trial approach [11,12], Exp [-ϕ(ξ)]-Expansion [13,14], a new auxiliary equation [15,16], Jacobi elliptic ansatz [17,18], generalized Bernoulli sub-ODE [19,20], functional variable [21,22], sub equation [23,24], and so on [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], have been established for efficient solutions of NLEs.…”

Section: Introductionmentioning

confidence: 99%

New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations

2020

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We solve distinct forms of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony [(3+1)-Dimensional WBBM] equations by employing the method of Sardar-subequation. When parameters involving this approach are taken to be special values, we can obtain the solitary wave solutions (sws) which is concluded from other approaches such as the functional variable method, the trail equation method, the first integral method and so on. We obtain new and general solitary wave solutions in terms of generalized hyperbolic and trigonometric functions. The results demonstrate the power of the proposed method for the determination of sws of non-linear evolution equations (NLEs).

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Section: Introductionmentioning

confidence: 99%

New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations

2020

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“…It is employed to find and study the wave solutions of the 2D-CNLS equation. The predominating equation is described by [29][30][31][32]:…”

Section: Introductionmentioning

confidence: 99%

“…The 2D-CNLS equation has been established by a one-dimensional reduction of the structure that defines the fractional quantum Hall effect (it is a quantum-mechanical version of the Hall effect existing in 2D electron systems related to strong magnetic fields and low temperatures). An extraordinary characteristic of Equation (1) is the nonlinearity of the current density, which informs the new execution for the SPM and self-focusing through the current [29][30][31][32]. This equation cannot pass the Painlevè test of integrability and is not invariant under the Galilean transformation [32].…”

Section: Introductionmentioning

confidence: 99%

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Different Types of Progressive Wave Solutions via the 2D-Chiral Nonlinear Schrödinger Equation

et al. 2020

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A versatile integration tool, namely the protracted (or extended) Fan sub-equation (PFS-E) technique, is devoted to retrieving a variety of solutions for different models in many fields of the sciences. This essay presents the dynamics of progressive wave solutions via the 2D-chiral nonlinear Schrödinger (2D-CNLS) equation. The solutions acquired comprise dark optical solitons, periodic solitons, singular dark (bright) solitons, and singular periodic solutions. By comparing the results gained in this work with other literature, it can be noticed that the PFS-E method is an useful technique for finding solutions to other similar problems. Furthermore, some new types of solutions are revealed that will help us better understand the dynamic behaviors of the 2D-CNLS model.

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“…Thus, the analytical techniques to derive traveling wave solutions for the governing models have to be proposed. Over the last few decades, numerous methods have been developed and applied to extract soliton solutions [31][32][33][34][35]. Hirota [36] extracted multiple collisions of soliton solutions of KdV equation.…”

Section: Introductionmentioning

confidence: 99%

Improved $\tan \left (\frac {\Phi (\xi )}{2}\right )$-Expansion Approach for Burgers Equation in Nonlinear Dynamical Model of Ion Acoustic Waves

et al. 2020

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The main purpose of this research is to find new and more exact traveling wave solutions of nonlinear dynamical model of ion acoustic waves in plasma with the help of famous reductive perturbation technique. A well-known nonlinear evolution equation, namely Burgers equation, is derived to investigate ion acoustic waves in relativistic plasma containing electrons and positrons. The traveling wave solution of Burgers equation is carried out by an affective integration tool, namely improved tan (ξ) 2 expansion method. As a result, different types of solutions such as periodic, kink, rational, exponential function, and hyperbolic function, are obtained. The wave profiles of solitary wave solutions are graphically depicted. The algorithm of the suggested technique is also outlined. It is admitted that the used method is efficient and influential tool for constructing solitary wave solutions of nonlinear evolution equations. Keywords Improved tan (ξ) 2-expansion approach • Ion acoustic shock waves • Weakly relativistic effects • Burgers equation

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Optical dark and dark-singular soliton solutions of (1+2)-dimensional chiral nonlinear Schrodinger’s equation

Cited by 106 publications

References 36 publications

New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations

New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations

Different Types of Progressive Wave Solutions via the 2D-Chiral Nonlinear Schrödinger Equation

Improved $\tan \left (\frac {\Phi (\xi )}{2}\right )$-Expansion Approach for Burgers Equation in Nonlinear Dynamical Model of Ion Acoustic Waves

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