Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation

Abstract

In this article, we employ the Mikhailov–Novikov–Wang integrable equation (MNWIE) appearing by means of the perturbatives symmetry approach to the rating of integrable non‐evolutionary PDEs. The new exact soliton solutions of this equation which were not achieved before have been realized for the first time in the framework of the (G′/G)‐expansion method. In the same vein and parallel, the corresponding numerical solutions of this equation have been established using the variational iteration method (VIM).

New diverse soliton solutions for the coupled Konno-Oono equations

“…(5) Some trials through few set of authors have been constructed to established different types of the soliton solutions for this model, sea for example, Alam and Belgacem [12] who constructed the exact solutions for this model using (G′/G)-expansion method, Yel, et al [13] who investigated the analytical solution of this model using the Sin-Gorden expansion method, Mirhosseini-Alizamini, et al [14] who applied the new extended direct algebraic method to constructed the exact solution for this model and Abdelrahman, et al [14] who applied the Jacobi-Elliptic functions to implemented the closed form of solutions for this model. In the same connection there are recent studies to obtain the traveling wave solutions for many nonlinear problems that arising in various branches of science has been listed through [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The main idea of this work is to achieve new visions for the different types of exact solutions of the NCKOM in terms of some variables through the manners mentioned above, whenever these variables take specific values, the solitary wave solutions could be achieved.…”

Dynamic nature of analytical soliton solutions of the (1+1)-dimensional Mikhailov-Novikov-Wang equation using the unified approach

“…Akbulut et al used the generalized Kudryashov method, exponential rational function method, and modified extended tanh-function method and obtained exact solutions [32]. With the help of the (G /G)-expansion method, Bekir et al obtained new exact soliton solutions of the MNW equation [33], whereas in this paper, we constructed new analytical soliton solutions with the aid of an effective and powerful unified method. Studying this equation can give a useful understanding of numerous impressive nonlinear scientific phenomena in oceanography and physics.…”

New lump solutions to the nonlinear Schrödinger equation under the few-cycle pulse propagation property

“…Hereby, constructing the lump solutions and other analytical travelling wave solutions of this model will add further future studies not only this propagation in metamaterials but also for all related phenomenon. The soliton behaviours and others travelling wave solutions to the suggested model that describing wave propagation in metamaterials will be show out via three powerful impressive techniques which are the (G'/G)-expansion method [21,22], the extended simple equation method [23][24][25] and the Paul-Painleve approach method [26][27][28]. Many new significant types of soliton solutions which were not realized before have been documented via these qualitative techniques.…”