A study on Caudrey–Dodd–Gibbon–Sawada–Kotera partial differential equation

Abstract

Bernoulli sub‐equation function method is applied to obtain exact solutions of Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) nonlinear partial differential equation. As a result of this, exact traveling‐wave and some new oscillating solutions to CDGSK are obtained. It may be observed that Bernoulli sub‐equation function method employed here is very effective and reliable to get explicit solutions for this nonlinear partial differential equation. Profiles of all constructed solutions are graphically illustrated entirely as well.

Optical solitons of Zoomeron equation by newly ϕ6-model expansion approach

“…( 53) for the parameters α 1 = 0.01, h 2 = −2.25, c = 1.2, w = 1.2, y = 1, z = 1. Figure [13] represents the 3D of the combined periodic solution of Eq. ( 54) for the parameters α 1 = 0.01,…”

“…This study's main motivation was the fact that partial differential equations (PDEs) regularly appear in the mathematical analysis of a range of problems in science and engineering and describe many fundamental natural principles [6]. It is now incredibly beneficial to look for precise answers to the both nonlinear evolution equations and partial differential equations NLEEs using a variety of techniques, and there are numerous effective techniques, such the inverse scattering transform approach [7], the Homoclinic technique [8], the sinh-Gordon function method [9], the generalized exponential rational function method [10], the auxiliary equation method [11], An alternative method [12], the Bernoulli sub-equation function method [13,14], the sub-equation analytical method [15], the modified sub-equation method [16], the auto-Bäcklund transformation method [17] and so on.…”

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

“…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],…”

Dynamical behavior for the approximate solutions and different wave profiles nonlinear fractional generalised Pochhammer-Chree equation in mathematical physics

“…First,ourself receive the solutions for existence and uniqueness. And other research solved timefractional generalised analytical-approximate solutions PC equations for waves publicity of an elastic rod using the q-homotopy analysis of the transform method [13][14][15], Modulation instability analysis [16], Hydro-magnetic [17], solitary wave [18], Carreau fluid [19], kink wave [20], Existence and Uniqueness [21,24], Hilbert space [22], natural reduced differential transform method [23], iterative Laplace transform method [25], tanh-coth and the sine-cosine methods [26], explicit fourthorder time stepping methods [27], decomposition method [28], weierstrass elliptic function method [30], modified F-expansion methods [31], global existence [32], generalized exponential rational function (GERF) technique [33][34], bernoulli sub-equation function method [35], lie group method [36], fractional natural decomposition method [37], modified exponential method [39], residual power series method [40], adams-bashforth scheme [41], laplace transform [42][43], conformable derivative [44,47], Mittag-Leffler function [45], caputo derivatives [46], Sumudu transform [48],and so on [49][50][51][52][53]…”