The effect of an electric field on the rotating flows of a thin film using a perturbation technique

Morad, Adel M.; Abu‐Shady, M.; Elsawy, G I

doi:10.1088/1402-4896/ab43ef

Cited by 6 publications

(2 citation statements)

References 29 publications

(54 reference statements)

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“…In recent years, the various applications of integrability and localized wave solutions of numerous NLPDEs can be noticed such as, the rogue wave and multiple lump solutions in the form of Grammian formula for the (2 + 1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation have been obtained by using polynomial function approach in [6]; multiple lump molecules and interaction solutions for the Kadomtsev-Petviashvili I equation are employed by utilizing non-homogeneous polynomial technique in [7]; lump chain solutions for the (2 + 1)dimensional BKP equation have been determined by using the τ-function in the form of Grammian formula in [8]; the soliton-cnoidal wave and lump-type solutions for (2 + 1)-dimensional KdV-mKdV equation are derived by utilizing Lie symmetry analysis and Bäcklund transformation approaches in [9]. The theoretical studies in nonlinear evolution equations have various applications in the diverse area of science and technology, such as: the electrohydrodynamics of a thin suspended liquid film model, which describes an incompressible fluid is examined by the perturbation technique in [10]; the granular model arising in the fluid dynamics has been solved by Painlevé analysis, Bäcklund transformation, Jacobi elliptic function, and tanh function methods in [11]; the magma equation arising in porous media is examined by the Cole-Hopf transformation method in [12]; the turbulent magnetohydrodynamic model in plasma turbulence has been solved using complex ansatz method in [13]; the compressible magnetohydrodynamic equations in cold plasma is examined by using the reductive perturbation method in [14].…”

Section: Introductionmentioning

confidence: 99%

New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

Singh¹,

Ray²

2023

Phys. Scr.

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Recognising the non-uniformity of boundaries and the inhomogeneities of media, nonlinear evolution equations with variable coefficients may display more realistic scenarios dealing with time-varying environments and inhomogeneous media. In this work, the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system that occurs in the domain of fluid dynamics is investigated. Painlevé analysis technique is used to demonstrate the integrability of the above mentioned system. The governing equations are revealed to be integrable in the Painlevé sense under no specific criterion on the variable-coefficients. To derive numerous analytical solutions, the auto-Bäcklund transformation (ABT) method is taken into account. Consequently, three different analytical solutions are found using the ABT technique, which include linear, exponential, rational, and complex solutions. All the solutions are displayed as 3D plots in which variable coefficients and parameters are varied to produce the desired results. These graphs depict the many aspects of the proposed coupled system in the various forms of periodic waves and complex periodic wave surfaces.

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Section: Introductionmentioning

confidence: 99%

New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

Singh¹,

Ray²

2023

Phys. Scr.

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“…In recent years, many scientific and industrial problems involve the flow of liquid thin films [11,12]. The stability of the thin film is of great significance in applications such as coating, adhesion, film morphology, optics, and sensors [13].…”

Section: Introductionmentioning

confidence: 99%

Effect of odd viscosity on the stability of thin viscoelastic liquid film flowing along an inclined plate

Zhao

Jian

2021

Phys. Scr.

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A theory for the stability of a viscoelastic film flowing along an inclined wall which is considered the odd viscosity effect is investigated. Using the lubrication theory, a new liquid-gas interface evolution equation involving odd viscosity effect is derived. Linear stability analysis shows that the larger odd viscosity leads to the higher critical Reynolds number. While the higher viscoelastic parameter makes the critical Reynolds number lower. The weakly nonlinear study reveals that in the limited amplitude range, the supercritical stable region and the explosion region will decrease with the increase of the odd viscosity. Conversely, the unconditional stable region and the subcritical unstable region increase. Interestingly, the threshold of the supercritical stable region decreases with the increase of the odd viscosity. Therefore, by analysing the linear and non-linear stability of the evolution equation, we find that the odd viscosity stabilizes the flow, while the viscoelastic property destabilizes the flow.

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Soliton, periodic and superposition solutions to nonlocal (2+1)-dimensional, extended KdV equation derived from the ideal fluid model

Rozmej,

Karczewska

2023

Nonlinear Dyn

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We present new (2+1)-dimensional extended KdV (KdV2) equation derived within an ideal fluid model. Next, we show several families of analytic solutions to this equation. The solutions are expressed by functions of argument $$\xi = (k x +l y-\omega t)$$ ξ = ( k x + l y - ω t ) . We found the soliton solutions in the form $$A\,\text {sech}^{2}(\xi )$$ A sech 2 ( ξ ) , periodic solutions in the form $$A\,\text {cn}^{2}(\xi ,m)$$ A cn 2 ( ξ , m ) and superposition solutions in the form $$\frac{A}{2}[\text {dn}^{2}(\xi ,m)\pm \sqrt{m}\,\text {cn}(\xi ,m)\text {dn} (\xi ,m)]$$ A 2 [ dn 2 ( ξ , m ) ± m cn ( ξ , m ) dn ( ξ , m ) ] analogous to the solutions of (1+1)-dimensional, extended KdV equation and to the solutions to ordinary Korteweg-de Vries equation. On the other hand, the existence of these families of analytical solutions for the highly nonlinear non-local (2+1)-dimensional, extended KdV equation is astounding. The existence of essentially one-dimensional solutions to the (2+1)-dimensional extended KdV equation explains the enormous success of the one-dimensional nonlinear wave equations for the shallow water problem.

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The effect of an electric field on the rotating flows of a thin film using a perturbation technique

Cited by 6 publications

References 29 publications

New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

Effect of odd viscosity on the stability of thin viscoelastic liquid film flowing along an inclined plate

Soliton, periodic and superposition solutions to nonlocal (2+1)-dimensional, extended KdV equation derived from the ideal fluid model

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