Studying on Kudryashov-Sinelshchikov dynamical equation arising in mixtures liquid and gas bubbles

Abstract

In this paper, some new exact traveling and oscillatory wave solutions to the Kudryashov-Sinelshchikov nonlinear partial differential equation are investigated by using Bernoulli sub-equation function method. Profiles of obtained solutions are plotted.

Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation

“…Step 4. Putting (7) and (8) in to ( 4) and combining all the phrases with the same power of E i equating to zero for i = 0, ∓1, ∓2, • • • , following the process will generate a system of algebraic equations that is solvable by using computer packages to obtain the values of the parameters.…”

“…Non-linearity theories depend heavily on analytical solutions to nonlinear partial differential equations (NPDEs) which can be used to interpret natural phenomena in physical and applied studies such as fluid mechanics, hydrodynamics, mathematical physics, optics, elasticated media, chemical reactions, astrophysics, ecosystems, quantum theory, geology, plasma physics, wave propagation, and shallow water [1][2][3][4][5]. Several methods for obtaining solutions of nonlinear partial differential equations have been improved recently, for instance, the method of the inverse scattering [6], the Bernoulli sub-equation function methods [7,8], and the use of the Laplace transformation for the system which involves the Caputo fractional derivatives [9]. To investigate the ion-acoustic wave constructions in plasma physics, the (3+1)dimensional gKdV-ZK equation is used which is taken in the following configuration [10,11],…”

Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons

“…The following non-topological wave ansatz [35] has been used in this section to find non-topological solutions for the equation (1),…”

“…Nonlinear differential equations arise in modeling several physical phenomena. These equations help handle the dynamics of the specific model [1][2][3]. Particularly interesting circumstances are modeled using nonlinear partial differential equations (NPDEs).…”

A Fixed Point Theorem for Time-Fractional Fornberg-Whitham Equation Arising in Atmospheric Science

“…Its non-linearity trait makes it very difficult to find an exact solution, and the discrete point findings of numerical approaches do not provide consistency. To address this problem, a number of researchers have provided techniques, such as the sine Gordon expansion method [16][17][18][19], the Homotopy analysis method [20][21], the Bernoulli sub-equation function method [22], the generalized exponential rational function method [23], the He's variational iteration method [24][25][26], the Homotopy perturbation technique [27][28][29], the Chebyshev spectral collocation method [30], the rational sine-cosine and rational sinh-cosh methods [31], the conformable derivative [32], the timefractional Caputo derivative [33], the Atangana-Baleanu derivatives [34], the fractional residual power series method [35], the Residual Power Series Method [36], semi-analytic technique to deal with nonlinear fractional differential equations [37]. For more details we can refer to [38].…”