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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 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 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]