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Nonlinear partial evolution equations are mostly significant to illustrate critical phenomena in wave theory concerning real-world problems. The current study deals with the (2 + 1)-dimensional nonlinear Fokas model depicting the nonlinear pulse through the mono-mode optical fibers. Improved auxiliary equation and improved tanh schemes are executed on the considering governing system. Subsequently, a variety of optical soliton solutions with the nature of dynamic nonlinear waves are made accessible throughout the present exploration. Some of constructed solutions are figured out in 3D, 2D and contour sense for the visualization to the readers for making them understand of the characteristics of dynamic waves. The solitons are visible to be bright, dark, kink, anti-kink, singular kink, periodic, compacton, anti-compacton etc. in the current exploration. Involved free parameters are assigned with various numerical values and brought out the effects of nonlinear pulses in wave propagation along mono-mode optical fibers. The entire work might claim to be recorded in the literature as new aspects of research. [ABSTRACT FROM AUTHOR]

Nonlinear evolution equations play enormous significant roles to work with complicated physical phenomena located across the nature world. The Schrödinger type equations bearing nonlinearity are important models that flourished with the wide-ranging arena concerning plasma physics, nonlinear optics, fluid flow and the theory of deep-water waves. In this exploration, we retrieve the soliton and other solutions in an appropriate form to the coupled nonlinear Schrödinger equations by means of the improved tanh method and the rational (G ′ / G) -expansion method. The suggested system of nonlinear Schrödinger equations is turned into a differential equation of a single variable through executing some operations. Thereupon, successful implementation of the advised techniques regains the abundant exact traveling wave solutions. The obtained solutions are figured out in the profiles of three-dimensional (3D), two-dimensional (2D) and contour by assigning suitable values of the involved unknown constants. These diverse graphical appearances enable the researchers to understand the underlying mechanisms of intricate phenomena of the leading equations. The individual performances of the employed methods are praiseworthy which deserve further application to unravel any other nonlinear partial differential equations arising in various branches of science. [ABSTRACT FROM AUTHOR]

Nonlinear evolution equations of arbitrary order bearing a significantly broad range of capability to illustrate the underlying behavior of naturalistic structures relating to the real world, have become a major source of attraction of scientists and scholars. In quantum mechanics, the nonlinear dynamical system is most reasonably modeled through the Schrödinger-type partial differential equations. In this paper, we discuss the (2+1)-dimensional time-fractional nonlinear Schrödinger equation and the (1+1)-dimensional space–time fractional nonlinear Schrödinger equation for appropriate solutions by means of the recommended enhanced rational (G ′ / G) -expansion technique adopting Cole–Hopf transformation and Riccati equation. The considered equations are turned into ordinary differential equations by implementing a composite wave variable replacement alongside the conformable fractional derivative. Then a successful execution of the proposed method has been made, which brought out supplementary innovative outcomes of the considered equations compared with the existing results found so far. The well-generated solutions are presented graphically in 3D views for numerous wave structures. The high performance of the employed technique shows the acceptability which might provide a new guideline for research hereafter. [ABSTRACT FROM AUTHOR]

Traveling wave solutions to nonlinear evolution equations (NUEEs) play a very important role in the area of applied mathematics, mathematical physics, and engineering. In this article, we suggest an extension of the (G'/G)-expansion method, called the rational (G'/G)-expansion method. The efficiency, usefulness, and capability of this method for providing traveling wave solutions have been demonstrated via the modified KdV-Burgers equation and the (2+l)-dimensional Boussinesq equation. The suggested method is reliable, competent and provides new general exact solutions than the existing methods. [ABSTRACT FROM AUTHOR]