Some new results of nonlinear model arising in incompressible visco‐elastic Kelvin–Voigt fluid

Abstract

The Oskolkov equation, which is a nonlinear model that describes the dynamics of an incompressible visco-elastic Kelvin-Voigt fluid, is examined in the present study. It has been obtained by applying the modified ( G ′ ∕G ) -expansion method, especially using calculation results such as kink wave, cusp wave, periodic respiratory waves, and periodic wave solutions. This research has employed this process to seek novel computational results of the Oskolkov equation. The dynamics of obtained wave solutions are analyzed and illustrated in figures by selecting appropriate parameters. With three dimensional, two dimensional, and contour graphical illustration, mathematical results explicitly exhibit the proposed algorithm's complete honesty and high performance in physics, mathematics, and engineering. KEYWORDS incompressible visco-elastic Kelvin-Voigt fluid, modified (G ′ ∕G)-expansion method, Oskolkov equation, wave solutions MSC CLASSIFICATION

Sıkıştırılamaz Visko Elastik Kelvin-Voigt Sıvısında Ortaya Çıkan Oskolkov Denkleminin Gezici Dalga Çözümleri

“…Different types of solutions of the Oskolkov equation have been obtained using different methods in the literature. For example; Alam et al have been presented periodic respiratory waves, kink wave, cusp wave and periodic wave solutions in their studies [1]. Roshid and Bashar have been presented kinky periodic wave and breather wave solutions using simple equation method [2].…”

“…Recently, there has been much concentration on NPEs in fields as diverse as fluid mechanics, signal processing, mathematical physics, chemical physics, plasma physics, optics, solid state physics, and geochemistry [1,2]. There are many methods for generating analytical solutions of NPEs have been employed successfully, such as tanh method [3], first integral method [4], new Kudryashov method [5], modified Kudryashov method [6], improved tanh method [7], sub-equation method [8], modified (1 / ) G -expansion method [9], auxiliary equation method [10], ansatz method [11],…”

“…The Oskolkov equation appears in various studies such as different types of traveling wave solutions of the Oskolkov equation have been investigated using the modified ( / ) GG  -expansion method [1], Ghanbari has been presented exact solutions for two Oskolkov-type equations [22], exact solutions have been attained for the Oskolkov equation [23], Thabet et al have been presented exact solutions for Oskolkov equations with exponential rational function method [24], Gozukızıl and Akcagıl have been created the exact solutions for the Oskolkov equation via tanh-coth method [25].…”

Simulation of a Combined (2+1)-Dimensional Potential Kadomtsev–Petviashvili Equation via Two Different Methods

“…The examination of solutions of these equations has become crucial across various fields of science and technology, including control theory, fiber optics, solid-state mechanics, transport infrastructure, atomic engineering, fluid dynamics, and various other research fields. Numerous successful approaches have been devised for investigating dynamic structures, such as lump solutions [1,2], the matrix eigenvalue problem [3], auto-Backlund transformations [4], the auxiliary equation method [5], the generalized Riccati equation mapping technique [6], the addendum to the Kudryashov technique [7], the unified method [8], the modified extended tanh-function approach [9], the Hirota bilinear technique [10], the Lie symmetry approach [11], the improved Bernoulli sub-equation function procedure [12], the modified (G ′ /G)-expansion method [13], the bilinear method [14], an extended (G ′ /G)-expansion method [15], the tanh-coth method [16,17], and so on.…”

Exact Solutions of M-Fractional Kuralay Equation via Three Analytical Schemes

“…Fractional partial differential equations (FPDEs) play an important role in many areas, including biology, applied physics, chemistry, economics, etc. Naturally occurring phenomena can be represented in the form of non-linear PDEs, i.e., the extended Zakharov-Kuzetsov equation [1], the fifth order Lax equation [2], the Fokas equation [3], the Clannish Random Walker's Parabolic equation [4], the Oskolkov equation [5], the Schrödinger dynamical system [6], the generalized unstable Schrödinger equation [7], the generalized Kadomtsev-Petviashvili modified equal-width dynamical equation [8], the dispersive long-wave equation [9], etc. There are many different schemes used to find the distinct types of exact solitons, including the improved generalized Riccati equation mapping method [10], Lie symmetry analysis [11], the generalized Jacobi elliptic function method [12], the exp-function method [13], the Khater method [14], the new modified simplest equation method [15], the new mapping method [16], the extended simplest equation method [17], the first integral method [18], the (ψ − φ)-expansion method [19], etc.…”