On solitons and invariant solutions of the Magneto-electro-elastic circular rod

New Interaction Solutions for a (2 + 1)-Dimensional Vakhnenko Equation

“…where ω 2 ≠ 0. Complexity e parameters in set (9) generate the following class of interaction solutions to equation (6) as…”

“…It is well known that nonlinear partial differential equations (NPDEs) and their solutions play a significant role in interpreting many important phenomena in nonlinear sciences. A variety of powerful methods are developed for finding the exact solutions of NPDEs, such as Hirota's method [1,2], simplified Hirota's method [3,4], the Lie symmetry analysis method [5,6], the simplest equation method [5,6], the invariant subspace method [7], and the nonlinear steepest descent method [8]. Very recently, the lump and interaction solutions [9][10][11] have attracted the attention of many scholars because of lump's applications in nonlinear optics, physics, oceanography, etc, and the interaction solutions are valuable in analyzing the nonlinear dynamics of waves in shallow water and can be used for forecasting the appearance of rogue waves [12,13].…”

Lomax Weibull Distribution

“…Due to its advantage in modelling lifetime data as compared to the other distributions, many researchers continue to develop modified versions of the general Weibull distribution with the aim of increasing its flexibility [4,5,6,7,8,9,10,[11][12][13][14][15]. An extensive review of modifications of the Weibull distribution together with expressions for the CDFs, PMF, or the PDF as well as the hazard functions was presented by [16].…”

On the Matlab Technique by Using Laplace Transform for Solving Second Order Ode With Initial Conditions Exactly

“…A transformations method can be used to get an exact solution to a differential equation. There are many methods which use transformation, Laplace transforms are commonly used in solving mathematical and physical problems which contains ordinary or partial differential equations with constant coefficients and integral equations as those problems are arising in the many branches of physics as electronic circuit analysis [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. But it takes too much time for solving by hand and in papers, These ODE can be analyzed.…”