New Soliton Solutions of The Nonlinear Radhakrishnan-Kundu-Lakshmanan Equation With the Beta-Derivative

In this article, the modified exponential function method is applied to find the exact solutions of the Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative. The definition of the conformable beta derivative and its properties proposed by Atangana are given. With the proposed method, exact solutions of the nonlinear Radhakrishnan-Kundu-Lakshmanan equation which can be stated with the conformable beta-derivative of Atangana are obtained. The exact solutions found as a result of the application of the method seem to be 1-soliton solutions, dark soliton solutions, periodic soliton solutions and rational function solutions. According to the obtained results, we can say that the Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative have different soliton solutions. Also, three-dimensional contour and density graphs and two- dimensional graphs drawn with different parameters are given of these new exact solutions.

Conservation laws, classical symmetries and exact solutions of a (1 + 1)-dimensional fifth-order integrable equation

In this paper, we present a study of a fifth-order nonlinear partial differential equation, which was recently introduced in the literature. This equation can be used as a model for bidirectional water waves propagating in a shallow medium. Using elements of an optimal system of one-dimensional subalgebras, we perform similarity reductions culminating in analytic solutions. Rational, hyperbolic, power series and elliptic solutions are obtained. Furthermore, by using the multiple exponential function method we obtain one and two soliton solutions. Finally, local and low-order conserved quantities are derived by enlisting the multiplier approach.

Analytical method for nonlinear mathematical models with Atangana conformable derivative

In this study, we investigate the analytical solutions of the modified Benjamin Bona Mahony and Sharma-Tosso-Olver equations, which are defined with Atangana conformable fractional derivative, using the modified exponential function method. Analytical solutions of the modified Benjamin Bona Mahony and Sharma-Tosso-Olver equations were obtained by using the modified exponential function method. Two, three-dimensional and contour graphics are used to understand the physical interpretations of the resulting analytical solutions to the mathematical model. When all these results and graphs are analzyed, it has been shown that the modified exponential function method is an effective method for obtaining analytical solutions for all other nonlinear fractional partial differential equations containing conformable fractional derivatives of Atangana.

Approximate Solution of Non-Linear Reaction-Diffusion in A Thin Membrane: Taylor Series Method

The nonlinear reaction-diffusion cycle in the thin membrane that describes the chemical reactions involving three species is studied. The model consists of the system of on nonlinear reaction-diffusion equations. The closed type of analytical expression of concentrations for the enzyme was developed by solving equations using the Taylor series formula. This results in the mixed Dirichlet and Neumann boundary conditions. Taylor series method similar to exponential function method. This technique provides approximate and simple solutions that are quick, easy to compute, and efficiently correct. These estimated findings are compared to the nuxmerical results. There is a good agreement with the simulation results.

Dark and trigonometric soliton solutions in asymmetrical Nizhnik-Novikov-Veselov equation with (2+1)-dimensional

In this manuscript, new dark and trigonometric function traveling wave soliton solutions to the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation by using the modified exponential function method are successfully obtained. Along with novel dark structures, trigonometric solutions are also extracted. For deeper investigating of waves propagation on the surface, 2D and 3D graphs along with contour simulations via computational programs such as Wolfram Mathematica, Matlap softwares and so on are presented.

FRACTIONAL CALCULUS OF THERMOELASTIC p-WAVES REFLECTION UNDER INFLUENCE OF GRAVITY AND ELECTROMAGNETIC FIELDS

In this paper, we discussed the longitudinal harmonic waves reflection from a solid elastic half-space with electromagnetic and gravity fields influence, considering a fractional order via fractional exponential function method. The clarifications are required for the reflection amplitudes ratios (i.e. the ratios between the reflected waves amplitude and the incident waves amplitude). The results obtained were calculated analytically and displayed by graphs to show the physical meaning of the phenomenon. A comparison has been made between the fractional and integer derivatives. The results of this paper demonstrate the rigor and effectiveness of the considered fractional technique.

A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation

In this article, some new travelling wave solutions of the (3+1) dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation are obtained using the modified exponential function method. When the solution functions obtained are examined, it is seen that functions with periodic functions are obtained. Two and three dimensional graphs of the travelling wave solutions of the BLMP equation are drawn by selecting the appropriate parameters

Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique

This paper is based on finding the exact solutions for Burger’s equation, Zakharov-Kuznetsov (ZK) equation and Kortewegde vries (KdV) equation by utilizing exponential function method that depends on the series of exponential functions. The exponential function method utilizes the homogeneous balancing principle to find the solutions of nonlinear equations. This method is simple, wide-reaching and helpful for finding the exact solution of nonlinear conformable PDEs.