Collisional Solitons Described by Two-Sided Beta Time Fractional Korteweg-de Vries Equations in Fluid-Filled Elastic Tubes

Abstract

This article deals with the basic features of collisional radial displacements in a prestressed thin elastic tube filled having inviscid fluid with the presence of nonlocal operator. By implementing the extended Poincare–Lighthill–Kuo method and a variational approach, the new two-sided beta time fractional Korteweg-de-Vries (BTF-KdV) equations are derived based on the concept of beta fractional derivative (BFD). Additionally, the BTF-KdV equations are suggested to observe the effect of related parameters on the local and nonlocal coherent head-on collision phenomena for the considered system. It is observed that the proposed equations along with their new solutions not only applicable with the presence of locality but also nonlocality to study the resonance wave phenomena in fluid-filled elastic tube. The outcomes reveal that the BFD and other physical parameters related to tube and fluid have a significant impact on the propagation of pressure wave structures.

Nonlinear complex generalized zakharov dynamical system inconformal sense utilizing new kudryashov method

“…Considering the rapid growth of symbolic computation systems, soliton solutions make it possible to analyze nonlinear physical phenomena; thus, examination of the soliton solutions for NLPDE has recently attracted the attention of researchers [1,2]. In the literature, there are diverse approaches applied by researchers to produce analytical solutions of NLPDE such as the first integral method [3,4], the extended Kudryashov technique [5], the Riccati Bernoulli sub-ODE scheme [6,7], the modified simple equation scheme [8], the extended rational sine-cosine and sinh-cosh method [9], the extended Poincare-Lighthill-Kuo method [10], the extended simplest equation method [11], traveling wave solution [12], the auxiliary ordinary differential equation method and the generalized Riccati method [13], the solitary wave solution technique with the…”

Analyzing the Kuralay-II equation: bifurcation, chaos, and sensitivity insights through conformable derivative and Jacobi elliptic function expansion

“…Due to their particle-like characteristics, optical solitons have been developed and used in telecommunications waveguides such as fibers and lasers [3][4][5][6]. Many methods have been used to solve nonlinear partial differential equations, including the Biswas-Milovic and Ginzburg-Landau equations [7][8][9][10][11].…”