New dynamical soliton propagation of fractional type couple modified equal-width and Boussinesq equations

Khatun, M. Ayesha; Arefin, Mohammad Asif; Islam, Mohammad Zohurul; Akbar, M. Ali; Uddin, M. Hafiz

doi:10.1016/j.aej.2022.03.033

Cited by 23 publications

(6 citation statements)

References 35 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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“…We wish to deal with simulating the growth of groundwater waves via a depth that is currently beyond the equal flow scale, which requires the presence of halfway coupled Boussinesq equation [38]…”

Section: Mathematical Analysismentioning

confidence: 99%

“…They look at the chaotic behavior of the system and qualitative behaviors of the dynamical system using the theory of planar dynamical model. Z Li et al [31], investigated the dynamical behavior of a time-space fractional Phi-4 model by utilising the bifurcation technique of a system with planar dynamics. MA YL et al [32], utilizing a system of planar dynamical and the tanh method, investigated the behavior of solitons with spatio-temporal dispersions of nonlinear Schrödinger equation with kerr medium.…”

Section: Introductionmentioning

confidence: 99%

Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model

et al. 2023

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In this work, we used the space-time fractional coupled Boussinesq (STFCB) model that is essential tools in the study of quantum optics, steady physics, the variational string's acoustic waves, ion vibrational frequencies, hydro-magnetic waves in cold plasma and many other fields.~In order to put such new precise solutions of the aforementioned model, the modified Sardar-sub equation (MSSE) technique has been suggested with inside the sense of conformable derivative and the fractional order partial differential equation that is capable of changing into an ordinary differential equation by using the travelling wave transform.~The scoring of solitons and other solutions demonstrates the MSSE technique compatibility for different constant values, which are shown in 3-D, 2-D and contour plots.~Additionally, we discussed the examined model chaotic and dynamical tendencies.~The theory of plane dynamical system is used to examine the chaotic patterns of the systems.~The investigations are novel and unexamined.~They can be utilized to explain the physical phenomena which have been simulated to provide details on the brief dynamical characteristics.~According to numerical simulations modifying the parameters of frequencies and amplitudes has an impact on the system of dynamical properties. We indicated that the MSSE technique for creating precise solutions offers new and significant mathematical tools in applied mathematics.

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“…Moreover, the homotopy perturbation Sumudu transform method was used to numerically obtain dark and bright solitons of the fractional MEW equation (Goswami et al ., 2019). Finally, the space-time fractional coupled MEW equation was explored in (Ayesha Khatun et al ., 2022).…”

Section: Introductionmentioning

confidence: 99%

On soliton solutions of the modified equal width equation

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et al. 2023

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PurposeThe soliton solutions are obtained by using extended rational sin/cos and sinh-cosh method. The methods are powerful and have ease of use. Applying wave transformation to the nonlinear partial differential equations (NLPDEs) and the considered equation turns into a nonlinear differential equation (NODE). According to the methods, the solution sets of the NODE are supposed to the form of the rational terms as sinh/cosh and sin/cos and the trial solutions are substituted into the NODE. Collecting the same power of the trigonometric functions, a set of algebraic equations is derived.Design/methodology/approachThe main purpose of this paper is to obtain soliton solutions of the modified equal width (MEW) equation. MEW is a form of regularized-long-wave (RLW) equation that represents one-dimensional wave propagation in nonlinear media with dispersion processes. This is also used to simulate the undular bore in a long shallow water canal.FindingsThus, the solution of the main PDE is reduced to the solution of a set of algebraic equations. In this paper, the kink, singular and singular periodic solitons have been successfully obtained.Originality/valueIllustrative plots of the solutions have been presented for physical interpretation of the obtained solutions. The methods are powerful and might be used to solve a broad class of differential equations in real-life problems.

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New dynamical soliton propagation of fractional type couple modified equal-width and Boussinesq equations

Cited by 23 publications

References 35 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

Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model

On soliton solutions of the modified equal width equation

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