Search

The fundamental intention of this article is to find several soliton solutions to the generalized Benjamin–Bona–Mahony equation. The fractional derivatives are described in the conformable sense. These solutions are generated using the functional variable approach. Then, we acquire via this technique some distinctive solutions, such as the singular soliton, periodic soliton, bell-shaped soliton, and kink soliton solutions. The fundamental feature of the demonstrated method is that it's convenient and provides precise, effective solutions to nonlinear equations. The solutions given will offer a thorough examination of this model and any associated occurrences. [ABSTRACT FROM AUTHOR]

The extended (2 + 1) -dimensional Calogero–Bogoyavlenskii–Schiff equation is investigated in this study. The extended (2 + 1) -dimensional Calogero–Bogoyavlenskii–Schiff equation is an extension of Calogero–Bogoyavlenskii–Schiff equation that describes the movement of Riemann waves along y-axis while long waves moves along the x-axis. The dynamics of Riemann waves is one of the most significant applications including tsunami in rivers, internal waves in oceans and magento-sound waves in plasmas. Finding new precise solutions with the assistance of a relatively new extended G ′ G 2 -expansion approach and exp (- φ (ζ)) -expansion technique is the primary objective of this effort. The suggested techniques are important tools in the fields of mathematical physics. Successful extraction of hyperbolic, rational, and trigonometric function solutions are achieved by using the proposed analytical methods. The extended (2 + 1) -dimensional Calogero–Bogoyavlenskii–Schiff equation is studied for the first time using extended G ′ G 2 -expansion approach and exp (- φ (ζ)) -expansion technique in this work and novel solutions are observed. 3D plots, contour plots and 2D plots are used to depict the dynamics of the extracted solutions. [ABSTRACT FROM AUTHOR]

In this study, we dealt with the new conservation theorem and the auxiliary method. We have applied the theorem and method to (3 + 1)-dimensional modified Wazwaz–KdV equations. When we applied a new conservation theorem to given equations, the obtained conservation laws did not satisfy the divergence condition. So, we modified the obtained conservation laws. These conservation laws contain extra terms. Finally, we applied the auxiliary method to given equations. We obtained two solution families with six exact solutions. All the obtained solutions are different from each other. For a suitable value of the solutions, the 3D and 2D surfaces have been plotted by Maple. [ABSTRACT FROM AUTHOR]

In this work, a variety of optical soliton solutions are derived for a nonlinear generalized equation with variable coefficients. At first, a computational approach is used to obtain solutions for the proposed model for a particular case. After, a generalized approach is considered to obtain other type of solutions given in a more general form. From the model considered here, the classical perturbed Fokas-Lenells equation is obtained and new optical soliton solutions for this last case are presented. Finally, some conclusions are given. [ABSTRACT FROM AUTHOR]

In this work, we investigate a new Kudryashov method (NKM) to find the exact and some new solutions of four different types of nonlinear Atangana conformable Boussinesq-like equations (NLACBEs). This is an appropriate algorithm for finding the exact solutions and also working for different types of nonlinear confirmable differential equations. In coastal and ocean engineering, some physical phenomenon is based on the exact solutions of the NLACBEs. [ABSTRACT FROM AUTHOR]

The aim of this work is to investigate new exact solutions of Tzitzéica type equations. We utilize the Painlevé transformation to transform the aforesaid non-linear evolution equations into ordinary differential equations. Then, the simplest equation method is employed for securing some real and complex solutions of the Tzitzéica equation, the Tzitzéica–Dodd–Bullough equation and the Dodd–Bullough–Mikhailov equation. After the execution of the simplest equation method, we obtain many new results more simply and reliably than the other approaches executed on these equations. The solutions are obtained and verified through soft computations. Also, the dynamics of some solutions are presented via three types of graphs including 2D, 3D and contour graphs. [ABSTRACT FROM AUTHOR]

In this paper, we use the new defined direct algebraic method based on some particular Riccati equations to find exact solutions to a Kaup–Newell model equation. Several new solutions which represent long waves parallel to the magnetic fields have been obtained. Many solutions in generalized hyperbolic and triangular function forms, exponential or logarithmic, are expressed explicitly. Most of the solutions determined in the study are new in the related literature. [ABSTRACT FROM AUTHOR]

In this present study, new sub-equation method is used to construct exact travelling wave solutions of the Cahn-Hilliard equation (CH). As a consequence, many new general exact travelling wave solutions are obtained including generalized hyperbolic (GH) function, generalized trigonometric (GT) function, exponential function and rational function solutions. Compared with the most existing similar new sub-equation method, the proposed method gives new and more general exact travelling wave solutions. More importantly, the method with the help of symbolic computation prepares a powerful mathematical tool for solving a great many nonlinear evolution equations in mathematical physics. [ABSTRACT FROM AUTHOR]