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This paper is performed to extract solitons and other solitary wave solutions of the generalized third-order nonlinear Schrödinger model by implementing two compatible schemes like improved auxiliary equation and enhanced rational (G ′ / G) -expansion methods. The mentioned equation governs extensive applications in numerous disciplines of engineering and applied science and demonstrate how short-ultra pulses in optical fibers and quantum characteristics interact dynamically. A stack of hyperbolic, rational, and trigonometric function solitary wave solutions is magnificently constructed by means of the indicated schemes. Some of the acquired wave solutions are characterized graphically in 3D outlines, contour forms and 2D shapes to illustrate the dynamical behavior. The density of nonlinearity is brought out by contour plots and 2D outlines make clear the dynamic nature of pulse transmission. A comparable analysis of this study with the available consequences in literature confirms the innovation and assortment of present accomplished wave solutions and hence enhances the great performance of the employed techniques. [ABSTRACT FROM AUTHOR]

Nonlinear models arise in numerous branches of science have become the core fascination of the scholars and scientists to illustrate the complexity of the real-life phenomena involved in the nature world. This paper is conducted to extract solitons and other solitary wave solutions of the generalized nonlinear Schrodinger model of order three through two influenced techniques namely, rational (G ′ / G) -expansion and improved tanh tools. The considered model governs wide ranging applications in numerous fields like short-ultra pulses in optical fibers. A heap of hyperbolic, rational, and trigonometric function solutions is successfully constructed by means of the suggested schemes in a decent manner. A few of the acquired outcomes are characterized graphically in 3D profiles, contour shapes and 2D outlines to describe the dynamical behavior. Contour plots describe the density of nonlinearity and 2D sketches make clear the dynamic nature of pulse propagation. A comparable experiment of the constructed results with the prevailing outcomes in literature establishes the novelty and diversity of our achieved solutions and hence confirms the high performance of the used tools as before. [ABSTRACT FROM AUTHOR]

This article deals with the nonlinear Kadomtsev–Petviashvili modified equal width (KP-mEW) equation used to model the matter-wave pulses, waves in ferromagnetic media, and long wavelength water waves with frequency dispersion and faintly nonlinear reinstating forces. The suggested model adopts a modification of the wave variable to make a single variable differential equation. Couple of competent techniques, notably the rational (G ′ / G) -expansion method and the improved tanh method is employed to extract wave solutions in appropriate form. Assorted typical and wide-spectral soliton solutions subject to rational, hyperbolic, and trigonometric functions and their integration are extracted successfully. To illustrate diverse soliton shapes, the obtained solutions are sketched in 3D, 2D, and contour profiles. The impact of velocity changes on soliton formation has also been the focus of this study. A comparative study of established results with existing results is performed, and the novelty of this study is shown. [ABSTRACT FROM AUTHOR]

Fractional nonlinear models involving the underlying mechanisms of numerous complicated physical phenomena arising in nature of real world have been taken major place of research arena during the couple of years for their significant roles. The study about the nonlinear optical and quantum context connecting to mostly Kerr law media as well as power law, dual-power law, triple-power law, saturable law, logarithm law and polynomial low is increasing at an inconceivable rate. In this exploration, the integrable generalized (2 + 1)-dimensional nonlinear Schrödinger system of equations in the sense of conformable fractional derivative is considered to unravel by means of two innovative schemes namely improved tanh method and rational G ′ / G -expansion method. The advised techniques are employed to seek for appropriate analytic wave solutions after converting the mentioned equation to an ordinary differential equation by introducing a wave variable alteration. The hyperbolic, trigonometric and rational function solutions are successfully gained and put forwarded for graphical representations. The assembled solutions are figured out in 3-D, 2-D and contour formats to illustrate their different views which appeared as kink type, anti-kink type, singular kink type, bell shape, anti-bell shape, singular bell shape, cuspon, peakon, periodic and singular periodic etc. The entire study bears the diversity and novelty of found solutions and applied techniques after making a comparable study with recent work recorded in the literature. [ABSTRACT FROM AUTHOR]