WICK-TYPE STOCHASTIC KdV EQUATION BASED ON LÉVY WHITE NOISE

Hyder, Abd‐Allah

doi:10.18642/jmsaa_7100121781

Cited by 4 publications

(3 citation statements)

References 22 publications

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“…In current eons, a diversity of potent schemes for attaining wave results of NPDEs have been offered, such as Hirota bilinear transformation, inverse scattering transformation, Bäcklund and Darboux transformation, the transformed rational function techniques, the tanh function method, the exp‐function scheme, sine‐cosine method, modified simple equation scheme, the elongated tribulation equation method, the ansatz approach, the Exp function method, homogeneous balance method, the tanh method, F‐expansion technique, ( G / G ′ )‐expansion technique, the modified tanh‐coth technique, sine‐cosine schemes, transformed rational function method, Sine–Gordon equation expansion scheme, 5–28 and many more 29–44 …”

Section: Introductionmentioning

confidence: 99%

Analytical wave solutions of the (2+1)‐dimensional Boiti–Leon–Pempinelli and Boiti–Leon–Manna–Pempinelli equations by mathematical methods

Seadawy

Ali

Helal

2021

Math Methods in App Sciences

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In this manuscript, with the successfully implementation of three mathematical methods, several types of exact and solitary wave solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) and (2+1)-dimensional of Boiti-Leon-Manna-Pempinelli (BLMP) equations are constructed. These schemes, namely called modified extended auxiliary mapping method, ameliorated form of simple equation and modified F-expansion. By transmission, the diverse values to the parameters, variants wave results are derived from exact peregrinating wave solution. Some solutions have been exemplified by graphical to understand the physical deportment of the BLP and BLMP wave models. The accomplished solutions seem with all essential constraint conditions, which are obligatory for them to subsist. Hence, our techniques via fortification of symbolic computations provide an active and potent mathematical implement for solving diverse benevolent nonlinear wave quandaries.

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Section: Introductionmentioning

confidence: 99%

Analytical wave solutions of the (2+1)‐dimensional Boiti–Leon–Pempinelli and Boiti–Leon–Manna–Pempinelli equations by mathematical methods

Seadawy

Ali

Helal

2021

Math Methods in App Sciences

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“…Wadati [37] first proposed and discussed the stochastic KdV equation and discussed the propagation of soliton of the KdV equation under the effect of Gaussian noise. Furthermore, Ghany and Hyder, [12,13,15,16] Chen and Xie, [5][6][7] Hyder and Zakarya, [26,27] and Hyder [24,25] investigated a wide class of Wick-type stochastic evolution equations by using different extension methods and white noise analysis. Recently, many research works have done to investigate the conformable PDEs and their exact solutions via various methods.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives

2020

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We deal with the Wick-type stochastic fractional Korteweg de–Vries (KdV) equation with conformable derivatives. With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.

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“…Wadati [11] first proposed and discussed the stochastic KdV equation and gave the propagation of soliton of the KdV equation under the effect of Gaussian noise. Furthermore, Ghany and Hyder [12][13][14][15], Ghany, Hyder and Zakarya [16,17], Chen and Xie [18][19][20], Hyder and Zakarya [21,22], Hyder [23,24], and Agarwal, Hyder and Zakarya [25] investigated a wide class of Wick-type stochastic evolution equations by using different extension methods and white noise analysis.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin–Bona–Mahony Equations

Agarwal

Hyder

Zakarya

et al. 2019

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In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin–Bona–Mahony (BBM) equations. We present a generalised version of the modified tanh–coth method. Using the generalised, modified tanh–coth method, white noise theory, and Hermite transform, we produce a new set of exact travelling wave solutions for the (3+1)-dimensional modified BBM equations. This set includes solutions of exponential, hyperbolic, and trigonometric types. With the help of inverse Hermite transform, we obtained stochastic travelling wave solutions for the Wick-type stochastic (3+1)-dimensional modified BBM equations. Eventually, by application example, we show how the stochastic solutions can be given as white noise functional solutions.

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WICK-TYPE STOCHASTIC KdV EQUATION BASED ON LÉVY WHITE NOISE

Cited by 4 publications

References 22 publications

Analytical wave solutions of the (2+1)‐dimensional Boiti–Leon–Pempinelli and Boiti–Leon–Manna–Pempinelli equations by mathematical methods

Analytical wave solutions of the (2+1)‐dimensional Boiti–Leon–Pempinelli and Boiti–Leon–Manna–Pempinelli equations by mathematical methods

Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives

Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin–Bona–Mahony Equations

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