Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

Akram, Ghazala; Mahak, Nadia

doi:10.1140/epjp/i2018-12061-7

Cited by 39 publications

(12 citation statements)

References 22 publications

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“…[19][20][21][22][23] However, there is no one-sizefits-all analytical technique for all nonlinear evolution problems. [24][25][26] In this context, we used the Khater II scheme to the 3-FNLS [27][28][29][30][31] to evaluate an unlimited number of solutions and then used the TQBS scheme 32,33 to determine the absolute value of error between the precise and numerical solutions. The three-FNLS equation is denoted by ref.…”

Section: Introductionmentioning

confidence: 99%

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Novel and accurate solitary wave solutions of the conformable fractional nonlinear Schrödinger equation

Zhao

Salama

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

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In this paper, the Khater II analytical technique is used to examine novel soliton structures for the fractional nonlinear third-order Schrödinger (3-FNLS) problem. The 3-FNLS equation explains the dynamical behavior of a system’s quantum aspects and ultra-short optical fiber pulses. Additionally, it determines the wave function of a quantum mechanical system in which atomic particles behave similarly to waves. For example, electrons, like light waves, exhibit diffraction patterns when passing through a double slit. As a result, it was fair to suppose that a wave equation could adequately describe atomic particle behavior. The correctness of the solutions is determined by comparing the analytical answers obtained with the numerical solutions and determining the absolute error. The trigonometric Quintic B-spline numerical (TQBS) technique is used based on the computed required criteria. Analytical and numerical solutions are represented in a variety of graphs. The strength and efficacy of the approaches used are evaluated.

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Section: Introductionmentioning

confidence: 99%

“…In this context, we used the Khater II scheme to the 3-FNLS 27-31 to evaluate an unlimited number of solutions and then used the TQBS scheme 32,33 to determine the absolute value of error between the precise and numerical solutions. The three-FNLS equation is denoted by ref.…”

Section: Introductionmentioning

confidence: 99%

Novel and accurate solitary wave solutions of the conformable fractional nonlinear Schrödinger equation

Zhao

Salama

et al. 2022

Journal of Low Frequency Noise, Vibration and Active Control

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“…A better deal of applications of NPDEs therefore appealed numerous researchers to look for their exact solutions. Many methods have been applied to find exact solutions of NPDEs such as, generalized exponential rational function [1], tanh method [2], the exp(−φξ)-expansion method [3], the extended rational sine-cosine approach and extended rational sinh-cosh approach [4,5], F-expansion method [6], extended Fan sub-equation method [7], the ( G ′ G )−expansion method [8], the first integral method [9,10], the unified method [11], the extended ( G ′ G 2 )−expansion method [12], the generalised unified method [13], hyperbolic and exponential ansatz methods [14], the Hirota bilinear [15], the ansatz method [16], the modified Kudryashov and new auxiliary equation methods [17], the general bilinear techniques [18], Sine-Gordon expansion method [19], the Hirota method [20], and so on.…”

Section: Introductionmentioning

confidence: 99%

Application of extended rational trigonometric techniques to investigate solitary wave solutions

Mahak

Akram

2021

Opt Quant Electron

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In this paper, a variety of novel exact traveling wave solutions are constructed for the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation via analytical techniques, namely, extended rational sine-cosine method and extended rational sinh-cosh method. The physical meaning of the geometrical structures for some of these solutions is discussed. Obtained solutions are expressed in terms of singular periodic wave, solitary waves, bright solitons, dark solitons, periodic wave and kink wave solutions with specific values of parameters. For the observation of physical activities of the problem, achieved exact solutions are vital. Moreover, to find analytical solutions of the proposed equation many methods have been used but given methodologies are effective, reliable and gave more and novel exact solutions.

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“…which is completely different from a list of conditions among p, q, r derived in [35]. For the condition (63), with the help of solutions (C-9) we obtain 10 new Jacobian elliptic solutions. For brevity we quote only following 3 new solutions…”

mentioning

confidence: 99%

“…-expansion method [64], the modified trigonometric function series method [65], the modified mapping method and the extended mapping method [66]. G. Akram et al [63] recently have successfully applied the extended G ′ /G 2 -expansion method and the first integral method on Eq. ( 68) to find some new exact solutions, which include hyperbolic function solutions, trigonometric function solutions, rational function solutions and soliton solutions.…”

mentioning

confidence: 99%

GiNaCDE: the high-performance F-expansion and First Integral Methods with C++ library for solving Nonlinear Differential Equations

Bairagi¹

2022

Preprint

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We present the algorithms for three popular methods: F-expansion, modified F-expansion, and first integral methods to automatically get closed-form traveling-wave solutions of nonlinear partial differential equations (NLPDEs). We generalize and improve the methods. The proposed algorithms are manageable, straightforward, and powerful tools providing a high-performance evaluation of the exact solutions of nonlinear ordinary differential equations (NLODEs) and NLPDEs. For differential equations with parameters, the new algorithms determine the conditions on the parameters to obtain exact solutions. The algorithms show solutions to a wide variety of NLODEs and NLPDEs, both integrable and non-integrable. It can solve NLODEs and NLPDEs that contain complex functions. The algorithms are implemented in a C++ library named GiNaCDE. The efficiency and effectiveness of the algorithms are demonstrated by some examples with the help of GiNaCDE. The output results tally with the previously known results, and in some cases, new exact traveling-wave solutions are explicitly obtained. Use of the library, implementation issues, scope, limitations, and future extensions of the software are addressed.

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Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

Cited by 39 publications

References 22 publications

Novel and accurate solitary wave solutions of the conformable fractional nonlinear Schrödinger equation

Novel and accurate solitary wave solutions of the conformable fractional nonlinear Schrödinger equation

Application of extended rational trigonometric techniques to investigate solitary wave solutions

GiNaCDE: the high-performance F-expansion and First Integral Methods with C++ library for solving Nonlinear Differential Equations

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