Analytical behavior of soliton solutions to the couple type fractional-order nonlinear evolution equations utilizing a novel technique

Zaman, U.H.M.; Arefin, Mohammad Asif; Akbar, M. Ali; Uddin, M. Hafiz

doi:10.1016/j.aej.2022.05.046

Cited by 30 publications

(5 citation statements)

References 32 publications

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“…Various approaches for discovering the analytical solutions of PDEs have been presented to overcome this issue. Some examples of the most significant methods are tanh-sech [1][2][3], extended tanh-function [4], the Sine-Gordon expansion [5], the trial function [6], the Darboux transformation [7], the Jacobi elliptic function [8,9], the sine-cosine [10,11], (G /G)-expansion [12,13], Hirota's function [14], exp(−φ(ς))-expansion [15], perturbation [16,17], the qualitative theory of dynamical systems [18][19][20][21], the direct method [22], the Riccati-Bernoulli sub-ODE [23], and the F-expansion method [24].…”

Section: Introductionmentioning

confidence: 99%

Multiplicative Brownian Motion Stabilizes the Exact Stochastic Solutions of the Davey–Stewartson Equations

2022

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In this article, the stochastic Davey–Stewartson equations (SDSEs) forced by multiplicative noise are addressed. We use the mapping method to find new rational, elliptic, hyperbolic and trigonometric functions. In addition, we generalize some previously obtained results. Due to the significance of the Davey–Stewartson equations in plasma physics, nonlinear optics, hydrodynamics and other fields, the discovered solutions are useful in explaining a number of intriguing physical phenomena. By using MATLAB tools to simulate our results and display some of 3D graphs, we show how the multiplicative Brownian motion impacts the analytical solutions of the SDSEs. Finally, we demonstrate the effect of multiplicative Brownian motion on the stability and the symmetry of the achieved solutions of the SDSEs.

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Section: Introductionmentioning

confidence: 99%

Multiplicative Brownian Motion Stabilizes the Exact Stochastic Solutions of the Davey–Stewartson Equations

2022

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“…In future work, we aim to study some other significant physical models that appear in nonlinear science to investigate the exact solutions with fractional solutions such that higher dimensional time fractional KdV-type equation [31], the time fractional third order time fractional modified KdV equation [32] and the space-time fractional coupled Whitham-Broer-Kaup (WBK) [33].…”

Section: Discussionmentioning

confidence: 99%

Wave solutions in (3 + 1)-dimensional generalized fractional mKdV-ZK equation utilizing jacobi elliptic functions

Elsadany,

Alshammari,

Elboree

2024

Phys. Scr.

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In this research, we investigate the e ects of fractional order on the (3 + 1)-dimensional general-ized space-time fractional modi ed KdV-Zakharov-Kuznetsov (mKdV-ZK) equation. We approachthe problem by utilizing the conformable fractional derivative. By reducing the mKdV-ZK equationto an integer order nonlinear ordinary di erential equation, we apply the Jacobi elliptic functionmethod to nd exact solutions. These solutions are speci cally tailored for the fractional order ofthe (3 + 1)-dimensional generalized mKdV-ZK equation, encompassing solitary waves, shock waves,and periodic waves. We also compare these exact solutions with fractional solutions to gain furtherinsights. Notably, our approach demonstrates the feasibility of solving nonlinear time-fractionaldi erential equations with conformable derivatives. Several diagrams have been included to visuallydepict the behavior of the solutions under fractional order when certain special parameter valuesare employed.

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“…In future work, the distributed multisensor fusion method can be applied to more elds. As the air tra c problem mentioned in [60][61][62], in order to avoid air accidents, this method can be used to install several sensors on the aircraft to avoid collisions, classify the objects, and track them.…”

Section: Discussionmentioning

confidence: 99%

Multisensor and Multitarget Tracking Based on Generalized Covariance Intersection Rule

Wang

Zhang

2022

Mathematical Problems in Engineering

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Distributed multitarget tracking (MTT) is suitable for sensors with limited field of view (FoV). Generalized covariance intersection (GCI) fusion is used to solve the MTT problem based on label probability hypothesis density (PHD) filtering in this paper. Because the traditional GCI fusion only has good fusion performance for the targets in the intersection of each sensor’s FoV, and the targets outside the intersection range would be lost, this paper redivides the Gaussian components according to the FoV and distinguishes the Gaussian components of the targets inside and outside the intersection. GCI fusion is sensitive to label inconsistency between different sensors. For label fusion in the intersection region, the best match of labels is found by minimizing label inconsistency index, and then GCI fusion is performed. Finally, the feasibility and effectiveness of the proposed fusion method are verified by simulation, and its robustness is proved. The proposed method is obviously superior to local sensor and traditional GCI algorithm.

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Analytical behavior of soliton solutions to the couple type fractional-order nonlinear evolution equations utilizing a novel technique

Cited by 30 publications

References 32 publications

Multiplicative Brownian Motion Stabilizes the Exact Stochastic Solutions of the Davey–Stewartson Equations

Multiplicative Brownian Motion Stabilizes the Exact Stochastic Solutions of the Davey–Stewartson Equations

Wave solutions in (3 + 1)-dimensional generalized fractional mKdV-ZK equation utilizing jacobi elliptic functions

Multisensor and Multitarget Tracking Based on Generalized Covariance Intersection Rule

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