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

Abstract

In this manuscript, exact solutions of the Oskolkov equation, which describes the dynamics of incompressible viscoelastic Kelvin-Voigt fluid, are presented. The -expansion method is used to search for these solutions. The dynamics of the obtained exact solutions are analyzed with the help of appropriate parameters and presented with graphics. The applied method is efficient and reliable to search for fundamental nonlinear waves that enrich the various dynamical models seen in engineering fields. It is concluded that the analytical method used in the study of the Oskolkov equation is reliable, valid and useful tool for created traveling wave solutions.

Optical solitons of the complex Ginzburg-Landau equation having dual power nonlinear form using $\varphi^{6}$-model expansion approach

“…As a result, a number of sophisticated mathematical techniques have been developed to generate soliton solutions for a wide range of physical models such as the Kadomtsev-Petviashvili equation [13], the Benjamin-Ono equation [14], the disturbance effect in intracellular calcium dynamic on fibroblast cells [15], the Fisher equation [16], the nonlinear Schrödinger equation [17,18], the Sharma-Tasso-Olver equation [19], the Murnaghan model [20], the Kaup-Kupershmidt equation [21], Navier-Stokes equation [22], the Zakharov-Kuznetsov equation [23], the B-type Kadomtsev-Petviashvili-Boussinesq equation [24] and others [25][26][27]. Recent analytical methods for solving PDEs, such as the eMETEM method [28], the generalized exponential rational function method [29], the extended sinh-Gordon equation expansion method [30], the q-homotopy analysis transform technique [31], the new extended direct algebraic method [32], the direct method [33], the Kudryashov's new function method [34], the split-step Fourier transform [35], the new modified unified auxiliary equation method [36], the 1 G ′ -expansion method [37][38][39], the Jacobi elliptic functions [40].…”