The Influence of Noise on the Solutions of Fractional Stochastic Bogoyavlenskii Equation

Al‐Askar, Farah M.; Mohammed, Wael W.; Albalahi, Abeer M.; El-Morshedy, Mahmoud

doi:10.3390/fractalfract6030156

Cited by 14 publications

(7 citation statements)

References 51 publications

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“…Bogoyavlenskii's breaking soliton equation was again derived by Xue and Gao [28] as a member of a (2+1) Schwarzian breaking soliton hierarchy, and its rational solutions were obtained. The equation also appeared in [29] as one of the equations associated with stochastic noise problems. The nonlinear dynamics of Bogoyavlenskii's breaking soliton equation is recently checked by Kumar and Manju [30].…”

Section: Exact Solution Of (2+1)-dimensional Breaking Soliton Equationmentioning

confidence: 99%

Novel solutions of (2+1) dimensional modified Bogoyavlenskii’s breaking soliton equation with variable coefficients

Wang

2023

Phys. Scr.

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In this paper, a (2+1)-dimensional breaking soliton equation is described. Firstly, the exact solution of the equation is constructed by the homogeneous equilibrium method. and the double soliton solutions with arbitrary functions are obtained. Second, the basic law of interaction between the different solitons are revealed and some new local structures are addressed by using the auxiliary equation method and the elliptic equation and the corresponding transformation, the infinite sequence exact solution of the generalized form equation of the breaking soliton equation is derived. Sinusoidal solitons, parabolic solitons and folded solitons of arbitrary shape propagating with variable speed are considered. In addition, by analyzing the infinite sequence of exact solutions given by the transformation of elliptic equation, the inner law between the exact solutions of the breaking soliton equation are also discussed.

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Section: Exact Solution Of (2+1)-dimensional Breaking Soliton Equationmentioning

confidence: 99%

Novel solutions of (2+1) dimensional modified Bogoyavlenskii’s breaking soliton equation with variable coefficients

Wang

2023

Phys. Scr.

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“…In order to obtain higher levels in chaos behaviour studies in plasma physics, nonlinear optical physics, shallow water waves and fluid mechanics, we investigate the following fractional stochastic Bogyavlenskie equation (FSBE) [18]:…”

Section: Introductionmentioning

confidence: 99%

Bifurcation, chaotic pattern and traveling wave solutions for the fractional Bogoyavlenskii equation with multiplicative noise

Han,

Jiang

2024

Phys. Scr.

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This paper presents a new study that incorporates the Stratonovich integral and conformal fractional derivative into the fractional stochastic Bogoyavlenskii equation with multiplicative noise. The study exposes the behavior of the system, including sensitivity, chaos and traveling wave solutions, by using the planar dynamical systems approach. Time series, periodic perturbation, phase portraits, and the Poincar'{e} section are used to comprehensively study the dynamic properties. Notably, the research uses the planar dynamic systems method to build multiple traveling wave solutions, including kink wave, dark soliton, and double periodic solutions. Furthermore, a comparative study approach is applied to investigate the effects of fractional derivative and multiplicative noise on the traveling wave solutions, which demonstrate a significant influence of both variables. This work demonstrates the creative application of the planar dynamic system method to the analysis of nonlinear wave equations, offering insightful information that may be generalized to more complex wave phenomena.

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“…[19], hyperbolic, trigonometric and rational function solutions of BE are constructed by using multiple expansion method. The researchers also used other methods to construct the exact solution of BE: modified extended tanh-function method [20], the first integral method [21], the extended Fan subequation techniqu [22], modified extended direct algebraic method [23] and exp(−Φ(η)) expansion method [24].…”

Section: Introductionmentioning

confidence: 99%

Chaotic behavior and exact traveling wave solutions for the fractional stochastic Bogoyavlenskii equation with multiplicative noise

Han

Zhang

Tang

2023

Preprint

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In this paper, the conformal fractional derivative and the Stratonovich integral are used to investigate the fractional stochastic Bogoyavlenskii equation with multiplicative noise. Using the dynamic system method, the chaotic behavior, sensitivity, and precise traveling wave solutions are provided. This study presents a complete investigation of the periodic, quasi-periodic, chaotic, and sensitive behavior using perturbations analysis, phase trajectory analysis, time series, and Poinca\'{r}e section. A number of novel traveling wave solutions are developed, including Jacobian elliptic functions, exponential and hyperbolic functions. The effect of multiplicative noise and fractional derivatives on the solution is then examined using a comparative analysis technique. The results show that the fractional derivative and random noise have a considerable impact on how the model behaves. The methods and results in this paper are useful and can be applied to studies of even more complicated phenomena.

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The Influence of Noise on the Solutions of Fractional Stochastic Bogoyavlenskii Equation

Cited by 14 publications

References 51 publications

Novel solutions of (2+1) dimensional modified Bogoyavlenskii’s breaking soliton equation with variable coefficients

Novel solutions of (2+1) dimensional modified Bogoyavlenskii’s breaking soliton equation with variable coefficients

Bifurcation, chaotic pattern and traveling wave solutions for the fractional Bogoyavlenskii equation with multiplicative noise

Chaotic behavior and exact traveling wave solutions for the fractional stochastic Bogoyavlenskii equation with multiplicative noise

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