Application of new Kudryashov method to various nonlinear partial differential equations

Malik, Sandeep; Hashemi, Mir Sajjad; Kumar, Sachin; Rezazadeh, Hadi; Mahmoud, Walaa H.; Osman, M. S.

doi:10.1007/s11082-022-04261-y

Cited by 118 publications

(29 citation statements)

References 62 publications

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“…The results are exhibited after a comprehensive analysis of the mathematical procedures that are detailed in the rest of the paper. Finally, there are many methods to discuss solutions to partial differential equations (PDEs), which have many applications in physics [27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

“…These soliton molecules form the information transporter across intercontinental distances around the world. Lastly, the nonlinear Schrödinger's equation (NLSE) has been discussed with help of many models [1–32, 33–36]. The aspect of stochastically is one of the features that is less touched, and there are a few papers that have discussed this aspect [3–9].…”

Section: Introductionmentioning

confidence: 99%

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Dispersive optical soliton solutions in birefringent fibers with stochastic Kaup–Newell equation having multiplicative white noise

Zayed,

El‐Horbaty,

Gepreel

2023

Math Methods in App Sciences

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In this article, we study for the first time the stochastic Kaup–Newell equation in birefringent fibers. Three integration algorithms are applied, namely, the unified Riccati equation expansion method, the addendum to Kudryashov's method, and the addendum to modified sub‐ODE method. Many types of optical soliton solutions such as Jacobi‐elliptic function solutions, Weierstrass elliptic function solutions, bright solitons, dark solitons, singular solitons, and periodic function solutions are obtained. Numerical schemes give a visual perspective to the solutions derived analytically.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dispersive optical soliton solutions in birefringent fibers with stochastic Kaup–Newell equation having multiplicative white noise

Zayed,

El‐Horbaty,

Gepreel

2023

Math Methods in App Sciences

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“…Ojha et al 46 explained viscoelastic hydromagnetic oscillatory flow in a channel in the presence of a sinusoidal pressure gradient and linear motion of the plate. Recently, various types of flow problems have been analyzed 47–60 …”

Section: Introductionmentioning

confidence: 99%

“…Recently, various types of flow problems have been analyzed. [47][48][49][50][51][52][53][54][55][56][57][58][59][60] The studies on the oscillating flow in a porous media are mainly focused on Newtonian fluids, and a corresponding problem for non-Newtonian fluids is in the much-to-be-desired state. The purpose of this paper is to study the oscillating flow of the viscoelastic fluid-saturated porous layer using the modified Oldroyd-B model.…”

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confidence: 99%

Viscoelastic effects on the oscillatory flow in a fluid‐saturated porous layer

Raghunatha,

Inc,

Vinod

2023

Heat Trans

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The oscillating flow of the viscoelastic fluid‐saturated porous layer has been useful in many areas, including the petroleum, chemical, and bioengineering industries. It is studied using the modified Darcy‐Oldroyd‐B model in this article. The exact solution is obtained utilizing a simpler and more reasonable method. According to this velocity solution, the time‐velocity profile of one kind of viscoelastic fluid is analyzed. From the analysis, it was found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Further, velocity, temperature, shear stress, and the rate of heat transfer are exponential solutions that are obtained and analyzed for different values of known physical parameters. Finally, we recognize that the relaxation and retardation parameters in this model act in the opposite manner.

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“…However, finding exact solutions to PDEs is generally more challenging than for ordinary differential equations due to the complexity of the equations and the increased number of variables involved. Analytical methods for PDEs include Lie symmetry method [9][10][11], reduction method [12,13], invariant subspace method [14][15][16], and Kudryashov method [17][18][19]. These methods involve advanced mathematical techniques and are essential in understanding various physical and natural phenomena, including fluid dynamics, heat transfer, and electromagnetic fields.…”

Section: Introductionmentioning

confidence: 99%

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Shehab,

El‐Sheikh,

Ahmed

et al. 2023

Math Methods in App Sciences

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The improved modified extended tanh‐function approach was used to study optical stochastic soliton solutions and other exact stochastic solutions for the nonlinear Schrödinger‐Hirota equation with multiplicative white noise. The derived solutions include stochastic bright solitons, stochastic singular solitons, stochastic periodic solutions, stochastic singular periodic solutions, stochastic exponential solutions, stochastic rational solutions, and stochastic Jacobi elliptic doubly periodic solutions. Constraints on the parameters were taken into account to ensure the existence of the obtained stochastic soliton solutions. Additionally, selected solutions were presented graphically to illustrate the physical characteristics of the stochastic solutions. In this paper, we used Mathematica (11.3) packages to find the coefficients and Matlab (R2015a) packages to plot the graphs.

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Application of new Kudryashov method to various nonlinear partial differential equations

Cited by 118 publications

References 62 publications

Dispersive optical soliton solutions in birefringent fibers with stochastic Kaup–Newell equation having multiplicative white noise

Dispersive optical soliton solutions in birefringent fibers with stochastic Kaup–Newell equation having multiplicative white noise

Viscoelastic effects on the oscillatory flow in a fluid‐saturated porous layer

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

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