Search

The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which is used to characterize the nonlinear behavior of magnets and describe how ferromagnetic materials are ordered is the main subject of this investigation. The system's dynamics are governed by the Schrödinger equation, which explains the variations in its quantum state over time. We implement two modern and efficient techniques, the improved auxiliary equation scheme, and the improved tanh method to find the exact solutions of HSFC model and develop travelling wave solutions in terms of rational, trigonometric, and hyperbolic functions with arbitrary parameters. Numerical findings are shown in 3-D plots, 2-D curves, and contours with carefully selected parametric values used to illustrate the dynamic wave shape using MATLAB software. The acquired results provide important insights into the physical implications of nonlinear dynamics in magnetic systems and significantly contribute to the understanding of electromagnetic wave models. The article finishes with a thorough appraisal of the physical interpretations generated from the obtained results. [ABSTRACT FROM AUTHOR]

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]

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]

Fractional order models involving nonlinearity are remarkable for having substantial application in real-world. The present determination is due to obtain applicable wave solutions of fractional order stochastic Bogoyavlenskii equation (SBE) in the viewpoint of stratonovich regarding multiplicative noise. Enhanced rational (G ′ / G) -expansion and improved auxiliary equation approaches are imposed to the suggested model which accumulate diverse wave solutions in appropriate form. The investigators might depict sophisticated tangible phenomena in a wide range with the assistance of the found well-furnished wave solutions as the governing equation makes understanding about the plasma physics, the wave of propulsion fluid-flow, and the dynamic characteristics of shallow-water waves. Various obtained solutions are figured out to portray prominent physical characteristics of nonlinear wave outlines. Different types of solitons are organized graphically in 3D shapes such as periodic, anti-periodic, compacton, anti-compacton, bell, anti-bell, peakon, kink, anti-kink, cuspon etc. Diverse 2D plots are comprised to make noticeable the wave velocity while contour plots signify the association among the concerned variables. The graphical representations are brought out together with the effects of noise strength and Brownian motion. The observation of the current whole work might captivate the researchers for future related work by employing the recommended approaches which are competent, pioneering, and concise. [ABSTRACT FROM AUTHOR]