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On the analytical soliton approximations to fractional forced Korteweg–de Vries equation arising in fluids and plasmas using two novel techniques

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Communications in Theoretical Physics 2024年第8期76卷 3-12页

作者： Weaam Alhejaili emad A az-zo.bi Rasool Shah S A El-Tantawy Department of Mathematical Sciences College of Science Princess Nourah bint Abdulrahman University Department Mathematics and Statistics Mutah University Department of Computer Science and Mathematics Lebanese American University Department of Physics Faculty of Science Port Said University Department of Physics Faculty of Science Al-Baha University

The current investigation examines the fractional forced Korteweg–de Vries(FF-KdV) equation,a critically significant evolution equation in various nonlinear branches of science. The equation in question and other associated equations are widely acknowledged for their broad applicability and potential for simulating a wide range of nonlinear phenomena in fluid physics, plasma physics, and various scientific domains. Consequently, the main goal of this study is to use the Yang homotopy perturbation method and the Yang transform decomposition method, along with the Caputo operator for analyzing the FF-KdV equation. The derived approximations are numerically examined and discussed. Our study will show that the two suggested methods are helpful, easy to use, and essential for looking at different nonlinear models that affect complex processes.

关键词： Caputo operator forced fractional KdV equation solitons Yang homotopy perturbation method Yang transform decomposition method

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Stability analysis and soliton solutions of the(1+1)-dimensional nonlinear chiral Schr?dinger equation in nuclear physics

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Communications in Theoretical Physics 2024年第9期76卷 1-15页

作者： Fazal Badshah Kalim U Tariq Ahmet Bekir S M Raza Kazmi emad az-zo.bi School of Electrical and Information Engineering Hubei University of Automotive Technology Department of Mathematics Mirpur University of Science and Technology Neighbourhood of Akcaglan Department of Mathematics and Statistics Faculty of Science Mutah University

The nonlinear Schr?dinger equation equation is one of the most important physical models used in optical fiber theory to explain the transmission of an optical soliton. The field of chiral soliton propagation in nuclear physics is very interesting because of its numerous applications in communications and ultra-fast signal routing systems. The (1+1)-dimensional chiral dynamical structure that describes the soliton behaviour in data transmission is dealt with in this work using a variety of in-depth analytical techniques. This work has applications in particle physics, ionised science, nuclear physics, optics, and other applied mathematical sciences. We are able to develop a variety of solutions to demonstrate the behaviour of solitary wave structures, periodic soliton solutions, chiral soliton solutions, and bell-shaped soliton solutions with the use of applied techniques. Moreover, in order to verify the scientific calculations, the stability analysis for the observed solutions of the governing model is taken into consideration. In addition, the3-dimensional, contour, and 2-dimensional visuals are supplied for a better understanding of the behaviour of the solutions. The employed strategies are dependable, uncomplicated, and effective; yet have not been utilised with the governing model in the literature that is now accessible. The resulting outcomes have impressive applications across a large number of study areas and computational physics phenomena representing real-world scenarios. The methods applied in this model are not utilized on the given models in previous literature so we can say that these describe the novelty of the work.

关键词： chiral solitons exact solutions solitons stability analysis the nonlinear Schrödinger equation

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Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-Ⅲ

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Computers, Materials & Continua 2023年第3期 5915-5930页

作者： Naret Ruttanaprommarin Zulqurnain Sabir Rafaél Artidoro Sandoval Nez emad az-zo.bi Wajaree Weera Thongchai Botmart Chantapish Zamart Department of Science and Mathematics Faculty of Industry and TechnologyRajamangala University of Technology Isan Sakonnakhon CampusSakonnakhon47160Thailand Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Department of Mathematical Sciences United Arab Emirates UniversityP.O.Box 15551Al AinUAE Universidad Nacional Autonoma de Chota CajamarcaPeru Department of Mathematics and Statistics Mutah UniversityMutah-Al Karak-Jordan Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand

The current research aims to implement the numerical resultsfor the Holling third kind of functional response delay differential modelutilizing a stochastic framework based on Levenberg-Marquardt backpropagationneural networks (LVMBPNNs). The nonlinear model depends uponthree dynamics, prey, predator, and the impact of the recent past. Threedifferent cases based on the delay differential system with the Holling 3^(rd) type of the functional response have been used to solve through the proposedLVMBPNNs solver. The statistic computing framework is provided byselecting 12%, 11%, and 77% for training, testing, and verification. Thirteennumbers of neurons have been used based on the input, hidden, and outputlayers structure for solving the delay differential model with the Holling 3rdtype of functional response. The correctness of the proposed stochastic schemeis observed by using the comparison performances of the proposed and referencedata-based Adam numerical results. The authentication and precision ofthe proposed solver are approved by analyzing the state transitions, regressionperformances, correlation actions, mean square error, and error histograms.

关键词： Holling 3^(rd)type delay factor mathematical model neural networks levenberg-marquardt backpropagation

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