ABSTRACT
The stochastic nonlinear Schrödinger model (SNLSM) in (1+1)-dimension with random potential is examined in this paper. The analysis of the evolution of nonlinear dispersive waves in a totally disordered medium depends heavily on the model under investigation. This study has three main objectives. Firstly, for the SNLSM, derive stochastic precise solutions by using the modified Sardar sub-equation technique. This technique is efficient and intuitive for solving such models, as shown by the generated solutions, which can be described as trigonometric, hyperbolic, bright, single and dark. Secondly, for obtaining numerical solutions to the SNLSM, the algorithms described here offer an accurate and efficient technique. Lastly, investigate the phase plane analysis of the perturbed and unperturbed dynamical system and the time series analysis of the governing model. The results show that the numerical and analytical techniques can be extended to solve other nonlinear partial differential equations in physics and engineering. The results of this study have a significant impact on how well we comprehend how solitons behave in physical systems. Additionally, they may serve as a foundation for the development of improved numerical techniques for handling challenging nonlinear partial differential equations.
Subject(s)
Algorithms , Engineering , Computer Simulation , Intuition , Physical ExaminationABSTRACT
The fractional coupled Konno-Onno model, which is frequently used in numerous fields of scientific and engineering disciplines, is being investigated in the current study in order to gain an understanding of complex phenomena and systems. The two main goals of this study are to be accomplished. Firstly, the research aims to identify novel solitons for the fractional coupled Konno-Onno model using the unified technique, which is currently absent from the literature. Secondly, a novel strategy that hasn't been previously investigated is phase portrait analysis for both perturbed and non-perturbed dynamical systems. The current study uses appropriate parametric values in phase plane analysis, 2D, 3D, and density plots to ensure the results are physically compatible. The results validate the claim that the technique used in this research to produce complete and uniform responses is not only simple to use and effective, but also substantially faster in computing. The technique is useful for resolving more complex phenomena that arise in engineering and mathematical physics.
Subject(s)
Engineering , PhysicsABSTRACT
In this research, we study traveling wave solutions to the fractional extended nonlinear SchrÖdinger equation (NLSE), and the effects of the third-order dispersion parameter. This equation is used to simulate the propagation of femtosecond, plasma physic and in nonlinear optical fiber. To accomplish this goal, we use the extended simple equation approach and the improved F-expansion method to secure a variety of distinct solutions in the form of dark, singular, periodic, rational, and exponential waves. Also, the stability of the outcomes is effectively examined. Several graphs have been sketched under appropriate parametric values to reinforce some reported findings. Computational work along with a graphical demonstration confirms the exactness of the proposed methods. The issue has not previously been investigated by taking into account the impact of the third order dispersion parameter. The main objective of this study is to obtain the different kinds of traveling wave solutions of fractional extended NLSE which are absent in the literature which justify the novelty of this study. We believe that these novel solutions hold a prominent place in the fields of nonlinear sciences and optical engineering because these solutions will enables a through understanding of the development and dynamic nature of such models. The obtained results indicate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable traveling wave solutions to nonlinear equations emerging in various branches of scientific, technological, and engineering domains.
ABSTRACT
In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.
ABSTRACT
In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature.
