Longitudinal strain waves propagating in an infinitely long cylindrical rod composed of generally incompressible materials and its Jacobi elliptic function solutions

Extraction Complex Properties of the Nonlinear Modified Alpha Equation

“…in which a 8 = 0, b = 0, d = 0. By getting the necessary derivations of Equation (33) for Equation (10), we report more new complex and rational wave solutions to the MAE, which these solutions produced by BSEFM. In this regard, this projected technique is a powerful tool for obtaining new analytical solutions for the nonlinear partial differential equations.…”

“…More general properties of auxiliary and sub-equation function methods have been comprehensively introduced in the literature [28,29]. Moreover, there are many published methods for solving similar equations using different techniques and methods [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49].…”

Soliton and Other Function Solutions of The Potential KdV Equation with Jacobi Elliptic Function Method

“…Many methods that yield soliton solutions are used to solve nonlinear partial equations, such as the extended tanh method [7], the first integral method [8], sine-Gordon expansion method [9], generalized tanh method [10], ' / GG method [11], Riccati method [12], Kudryashov method [13,14], the F-expansion method [15] etc.…”

Değişken katsayılı çok boyutlu dalga benzeri denklemler için kesirli yaklaşım üzerine etkili bir metot

“…Recently, many authors investigated many mathematical models exemplifying real world problems with the help of fractional calculus, for instance the mathematical model of HIV-1 infection of CD4+T-cells with conformable fractional operator is investigated in [26], the model arising in falling film problems is numerically studied by authors in [27] using two novel techniques, fractional SIR epidemic model of childhood disease examined with the help of Mittag-Leffler memory in [28], some interesting results integro-differential equation of fractional order ith state dependent delay are derived in [29], nondensely characterized integro-differential equations are studied by authors in [30], the numerical stimulation is presented by researchers in [31] for the coupled fractional Whitham-Broer-Kaup equations describing the propagation shallow water waves, by using Hilfer fractional derivative scholars in [32] derived some stimulating results, by using two different algorithms authors in [33] find the solution for Fokas-Lenells equation, authors in [34] presented the numerical stimulation for the nonlinear equations occurs in ion acoustic waves in plasma with Mittag-Leffler law, and many research considered FC has tool with its fundamental notions and results to derive some essential and stimulating results [35][36].…”

“…For instance, the vibrations of acoustic or string waves in a pipe and the velocity of the wave are evaluated by the physical properties of the material through which it propagates. These equations are also employed to study and analyse fluid migration at depth in the crust through fluidsaturated porous media [36], coupling currents in a flat two-layere multi-strand cable having superconductivity [37], elastic waves in soils with non-homogeneous [38] and earthquake stresses [39]. By the aid of single wave-like equation with time-dependent in the flat cables associated with the magnetic field, the gradually decaying long current loops with the additional established effects are illustrated [37].…”