Soliton solutions of the resonant nonlinear Schrödinger equation using modified auxiliary equation method with three different nonlinearities

Akram, Ghazala; Sadaf, Maasoomah; Khan, M. Atta Ullah

doi:10.1016/j.matcom.2022.10.032

Cited by 38 publications

(3 citation statements)

References 18 publications

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“…These methodologies encompass a variety of approaches, including the unified auxiliary equation method used by Mathanaranjan et al [22], the sine-Gordon expansion method [23], the simple extended [24], the bilinear neural network method [25], variational iteration techniques [26], the extended exponential function technique [27], the power series methodology [28], the Hirota bilinear technique [29]. Numerous others [30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

Majid,

Asjad,

Faridi

2024

Phys. Scr.

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This article investigates the non-linear generalized geophysical KdV equation, which describes shallow water waves in an ocean. The proposed generalized projective Riccati equation method and modified auxiliary equation method extract a more efficient and broad range of soliton solutions. These include U-shaped, W-shaped, singular, periodic, bright, dark, kink-type, breather soliton, multi-singular soliton, singular soliton with high amplitude, multiple periodic, multiple lump wave soliton, and flat kink-type soliton solutions. The travelling wave patterns of the model are graphically presented with suitable parameter values using the modern software Maple and Wolfram Mathematica. The visual representation of the solutions in 3D, 2D, and contour surfaces enhances understanding of parameter impact. Sensitivity and modulation instability analyses were performed to offer insights into the dynamics of the examined model. The observed dynamics of the proposed model were presented, revealing quasi-periodic chaotic, periodic systems, and quasi-periodic behaviour. This analysis confirms the effectiveness and reliability of the method employed, demonstrating its applicability in discovering travelling wave solitons for a wide range of nonlinear evolution equations.

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Section: Introductionmentioning

confidence: 99%

Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

Majid,

Asjad,

Faridi

2024

Phys. Scr.

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“…used toobtain exact solitonsolutions for non-linear partial differential equations, [30] variational iteration method [31], extended exponential function method [32], Hirota bilinear technique [33], power series method [34], F-expansion technique [35] as well as several others [36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Asjad¹,

Ashaq²,

Faridi³

et al. 2023

Preprint

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In this article, the new extended direct algebraic method is used to build the exact travellingwave solutions for the non-linear time-fractional Clannish Random Walker’s Parabolic equation.This study establishes the framework in which periodic, singular, dark, bright and kink-typewave solitons are obtained with exact solutions offered by the mixed hyperbolic and trigonom-etry solutions, mixed periodic and periodic solutions, plane solutions, shock solutions, mixedtrigonometric solutions, mixed singular solutions, mixed shock single solutions, complex solitarysingular solutions, shock solutions and shock wave solutions. The exact soliton solutions of thetime-fractional clannish random walker’s parabolic equation model is graphically presented atdifferent values of involved parameters by Wolfram Mathematica software. The propagating behaviours display in 3-D, contour and 2-D surfaces of the obtained results to visualise the im-pact of the involved parameters. The sensitivity analysis is demonstrated for the wave profilesof the designed dynamical framed structure, where the soliton wave number parameter regulatesthe water wave singularity. This analysis illustrates that the utilized method is efficient andreliable and can be useful to find appropriate solutions in closed-form solitary soliton to a wide range of non-linear evolution equations. These techniques can also be utilised to find new exact travelling wave solutions for any class of integer or fractional differential equations thatarise in mathematical physics.

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“…Nonlinear partial differential equation (NLPDEs) perform a main role in different branches of physics and mathematics engineering, such as optical fibers, meteorology, fluid dynamics, chemical physics, theory of turbulence, solitary wave theory, among other fields [1]- [18]. Daring the previous decades, multiple impactful techniques are presented in order to get exact solutions for NLPDEs, such as the inverse scattering transform method [1], Kudryashov's method [2], (G ′ /G) -expansion method [3] , the sub -ODE [4] , an extended improved tanh -function method [5], auxiliary equation method [6], the solitary wave ansatz method [7], He's variational method [8], new modified extended direct algebraic [9] and lots of other [10]- [15].…”

Section: Introductionmentioning

confidence: 99%

The Hyperbolic Function Method for the Fractional (3+1)-Dimensional Generalized Korteweg-De-Veies-Zakharov-Kuznetsov Equation in Plasma Physics

Torvattanabun,

Boonprasop,

Phunphon

et al. 2023

Int. J. of Appl. Math.

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The fractional (3+1)-dimensional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) is one of the nonlinear models to indicate the impact of magnetic fields on weak ion-acoustic wave in plasma comprised of cool and hot electrons. We have applied the hyperbolic function method to explore the diversity of wave structures. We extract the solitons in form of bright solitons, dark solitons, bright-dark combo solitons and other solitons. Moreover, for the physical illustration, some of the obtained solutions are represented graphically.

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Soliton solutions of the resonant nonlinear Schrödinger equation using modified auxiliary equation method with three different nonlinearities

Cited by 38 publications

References 18 publications

Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

The Hyperbolic Function Method for the Fractional (3+1)-Dimensional Generalized Korteweg-De-Veies-Zakharov-Kuznetsov Equation in Plasma Physics

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