New impressive behavior of the exact solutions to the Benjamin-Bona-Mahony-Burgers equation with dual power-law nonlinearity against its numerical solution

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.…”

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

“…Indeed, we concentrate our attention on the nonlinear Schrödinger equation that models the dynamic of waves in such materials. The arising solitons and other analytical solutions to different forms of Schrödinger models have been widely studied by the authors [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The few-cycle pulse propagation in metamaterials specially is one of nonlinear Schrödinger applications and its solutions are helpful to understands more deeply the concerned materials.…”

New Variety Types of Solution to the Fujimoto-Watanable Equation With the Corresponding Numerical Solutions

“…The RBSODM [6] is the only one of the ansatze methods that doesn't depend on the balance rule has been used effectively to obtain impressive description to the exact solutions to this equation. The homogeneous balance fails of this equation, hence all the ansatze approaches methods [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] that depend on this rule will be fail to realize any solution for this equation. In addition, we will apply the VIM [23][24] to demonstrate the identical numerical solutions for all achieved solutions of this equation.…”