No abstract

In this work, the new optical soliton solutions and interaction solutions for the space-time fractional Fokas–Lenells equation with fractional [Formula: see text]-derivatives are constructed via three mathematical analytical techniques, namely the extended SE method, unified solver method, and three-wave methods. The results have proved the efficiency of the suggested techniques for obtaining abundant optical soliton solutions to nonlinear evolution equations (NLEEs) and closed-form solutions in the forms of rational function solutions; hyperbolic and trigonometric function solutions and multi-wave interaction solutions are obtained. These techniques are more efficient, robust, and powerful mathematical tools for acquiring several optical soliton solutions for many other fractional space-time NLEEs that arise in optical physics and plasma physics. The graphical representations of the combined optical solitons are demonstrated using three- and two-dimensional graphics.

Methods known as fractional subequation and sine-Gordon expansion (FSGE) are employed to acquire new exact solutions of some fractional partial differential equations emerging in plasma physics. Fractional operators are employed in the sense of conformable derivatives (CD). New exact solutions are constructed in terms of hyperbolic, rational, and trigonometric functions. Computational results indicate the power of the method.

This research finds an equation in a continuous domain and a discrete equation governing the system of cold bosonic atoms (CBA) in a zigzag optical lattice using a continuum approximation. Many solutions to the equation were obtained using two distinct methods: the three-wave approach (multi-wave interaction, rational solutions, and rational solution interaction) and the extended sub-equation method. These analytical approaches are more effective, consistent, and comprehensive mathematical tools for obtaining various exact closed-form solutions for a wide range of fractional space-time nonlinear evolution equations encountered in optical physics, condensed matter physics, and plasma physics. The solutions generated are in the form of hyperbolic and trigonometric solutions, and other-form solutions are obtained. Three-dimensional graphics and contour plots are often used to depict the graphical representations of the combined soliton solutions. These findings will aid our understanding of the dynamics of the zigzag optical grids and many other structures formed by colder bosonic atoms. The applied approaches are more simple, efficient, and straightforward to obtain the closed-form solutions for various nonlinear evolution equations in the fields of nonlinear sciences and physical engineering.

Here, the Deoxyribo-Nucleic Acid (DNA) dynamic equation that arises from the oscillator chain named the Peyrard-Bishop model for plenty of solitary wave solutions is presented. The efficacy of newly designed algorithms are investigated, namely, the extended Auxiliary equation method and Kudryashov expansion method for constructing the new solitary wave solutions of the DNAdynamic Peyrard-Bishop model with beta-derivative. Here, the proposed methods contribute to a range of accurate solutions for soliton, including light, dark, and other solutions are obtained. In addition, some results are also clarified by computer simulations demonstrating the uniqueness of our work relative to the existing literature on the classic Peyrard-Bishop model. These solutions lead to the issue of the possibility to expand the method to deal with other non-linear equations of fractional space-time derivatives in non-linear science. It is noted that the newly proposed approach is accurate and is used to create new general closed-form solutions for all other fractional NPDEs.