Bifurcation Analysis of Travelling Waves and Multi-rogue Wave Solutions for a Nonlinear Pseudo-Parabolic Model of Visco-Elastic Kelvin-Voigt Fluid

Abstract

Through this article, we focus on the extension of travelling wave solutions for a prevalent nonlinear pseudo-parabolic physical Oskolkov model for Kevin-Voigt fluids by using two integral techniques. First of all, we explore the bifurcation and phase portraits of the model for different parametric conditions via a dynamical system approach. We derive smooth waves of the bright bell and dark bell, periodic waves, and singular waves of dark and bright cusps, in correspondence to homoclinic, periodic, and open orbits with cusp, respectively. Each orbit of the phase portraits is envisaged through various energy states. Secondly, with the help of a prevalent unified scheme, an inventive version of exact analytic solutions comprising hyperbolic, trigonometric, and rational functions can be invented with some collective parameters. The unified scheme is an excitably auspicious method to procure novel interacting travelling wave solutions and to obtain multipeaked bright and dark solitons, shock waves, bright bell waves with single and double shocks, combo waves of the bright-dark bell and dark-bright bell with a shock, dark bell into a double shock wave, and bright-dark multirogue type wave solutions of the model. The dynamics of the procured nonlinear wave solutions are also presented through 2-D, 3-D, and density plots with specified parameters.

Dynamics and Soliton Propagation in a Modified Oskolkov Equation: Phase Plot Insights

“…Various techniques have been employed in the works of different researchers. Roshid and Roshid [17] examined Equation ( 1) by adopting a simple equation technique and obtained various soliton patterns, Karakoc et al [18] investigated Equation ( 2) by employing the finite element approach, Ghanbari [19] obtained traveling wave profiles for Equations ( 1) and ( 2) by using modified methodology, Kaplan et al [20] implemented the exponential rational function approach and discussed the sensitivity of Equations ( 1) and ( 2), and Uddin et al [21] analyzed the dynamic behavior and discovered traveling waves and rouge wave solutions of Equation ( 1) by adopting the unified technique.…”

Exact Solutions of an Extended Jimbo-Miwa Equation by Three Distinct Methods

“…So far, mathematicians and physicists have established several efective methods, such as F-expansion method, [19][20][21] the frst integral method, [22] dynamical system method, [23,24] improved Kudryashov method, [25][26][27] Hirota bilinear approach, [28][29][30][31] tan(Θ/2) expansion approach, [32] exp (− ϕ(ξ))-expansion method, [33] generalized exponential rational function method [34], and other methods [35]. Te (G ′ /G)-expansion method proposed by Wang et al [36] is one of the most efective direct methods to obtain travelling wave solutions of a large number of nonlinear evolution equations, such as the KdV equation, the mKdV equation, the variant Boussinesq equations, the Hirota-Satsuma equations, and so on.…”

New Exact Solutions of the Drinfeld-Sokolov System by the Generalized Unified Method

“…In this paper, we have applied the GUM [19] to derive exact solutions for the DSS. The GUM is an enhanced version of the unified method [20,21] that many authors [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] have successfully applied to solve different types of NPDEs. Compared with other methods, the GUM requires less computational work with high reliability to solve NPDEs.…”