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Article
Engineering, Marine
Asim Zafar et al.
Summary: The investigation of exact solitary wave solutions to the nonlinear partial differential equation is crucial for understanding physical phenomena in various applied fields. This study explores the van der Waals model using two novel integration approaches, the simplest equation method and the expa function method, and discovers new solitary waves and exact solutions. The results demonstrate that these approaches are simple and effective for dealing with nonlinear models.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2022)
Article
Engineering, Marine
Sachin Kumar et al.
Summary: This paper investigates a nonlinear equation that describes fluid propagation and obtains the exact closed-form solutions using two efficient methods. These methods prove to be effective, authentic, and straightforward mathematical tools for obtaining closed-form solutions to nonlinear partial differential equations.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2022)
Article
Engineering, Marine
Marwan Alquran et al.
Summary: This paper investigates new wave solutions for the modified-mixed KdV equation and bidirectional waves for the Benjamin Ono equation using extended rational sine-cosine and sinh-cosh methods. Different types of soliton solutions are categorized and analyzed with 2D and 3D graphs. Additionally, some physical properties of the new bidirectional waves solutions to the Benjamin Ono model are discussed.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2022)
Article
Mathematics, Interdisciplinary Applications
Fuzhang Wang et al.
Summary: This paper presents a numerical solution method for nonlinear time-fractional Fisher equations using a local meshless method combined with explicit difference scheme. Radial basis functions are used to compute space derivatives, and the Caputo derivative scheme is used for time-fractional integration. The accuracy is evaluated using the maximum error norm, and the method is validated with non-rectangular domains.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Physics, Applied
U. Younas et al.
Summary: This paper focuses on the nonlinear dynamics of solitary waves in the phase separation kinetics of iron (Fe-Cr-X(X = Mo, Cu)) based on ternary alloys. The convective-diffusive Cahn-Hilliard equation is used as a mathematical model to describe the dynamics of phase separation. Various solitary wave solutions with unknown parameters are obtained using computational tools such as the extended Fan-sub equation method and extended auxiliary equation method. The results demonstrate that these computational methods are direct, dynamic, and well organized, making them useful for solving complex nonlinear problems in different areas.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2022)
Article
Physics, Applied
U. Younas et al.
Summary: This paper focuses on the nonlinear dynamical behavior of ultra-short pulses in optical fiber. Different types of soliton solutions are obtained by using the new Hamiltonian amplitude equation and three computational integration techniques. The results demonstrate that the examined equation contains various soliton solution structures and the methods used are concise and efficient, with potential applications in understanding energy transit and diffusion processes in nonlinear optics. A comparison with existing literature is provided.
MODERN PHYSICS LETTERS B
(2022)
Article
Engineering, Electrical & Electronic
Usman Younas et al.
Summary: This manuscript investigates the propagation behavior of nonlinear waves in the elastic Murnaghan's rod and extracts various solitary wave solutions in different shapes. The results obtained are new and have significant application value.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Mathematics
Zai-Yin He et al.
Summary: This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination and examines its dynamical behavior analytically and numerically. It is verified that the introduced fractional discrete SIR epidemic model with both commensurate and incommensurate fractional orders exhibits chaotic behavior. The discrete fractional model displays more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders.
Article
Materials Science, Multidisciplinary
Usman Younas et al.
Summary: The main focus of this article is to investigate the abundant new soliton solutions in ferrite materials. The Kraenkel-Manna-Merle (KMM) system is used as a governing model, and the Phi(6)-model expansion method is applied to analyze the model. The results show that the obtained solutions have very rich soliton structures.
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Md Ashik Iqbal et al.
Summary: In this article, exact dynamical wave solutions to the Date-Jimbo-Kashiwara-Miwa equation with conformable derivative are constructed using the two-variable G'/G, 1/G-expansion method. The solutions are classified and analyzed, and the effect of the fractional parameter on the solutions is discussed.
FRACTAL AND FRACTIONAL
(2022)
Article
Engineering, Marine
A. A. Gaber
Summary: In this study, the (2+1)-dimensions of dispersive long wave equations on shallow waters, known as the Wu-Zhang (WZ) equations, were investigated using symmetry analysis. The system of partial differential equations was reduced to ordinary differential equations, and exact solutions including singular wave, kink wave, and anti-kink wave were obtained using the general Kudryashov method [2]. Figures were provided to demonstrate the properties of the solutions.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2021)
Article
Multidisciplinary Sciences
Abdulla-Al-Mamun et al.
Summary: The study explores exact singular, solitary, and periodic wave solutions for the newly implemented 3D fractional WBBM equation family through the (G'/G(2))-expansion process. Various trigonometric, complex hyperbolic, and rational functions are utilized to obtain these solutions using computational software Mathematica.
Article
Mathematics, Applied
Mostafa M. A. Khater et al.
Summary: This manuscript applies the TQBS scheme to investigate the numerical solution of the conformable fractional nonlinear time-space telegraph equation and constructs exact traveling wave solutions using three computational schemes. The most accurate numerical scheme among the three applied schemes is illustrated.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Materials Science, Multidisciplinary
U. Akram et al.
Summary: In this manuscript, an extended modified auxiliary equation mapping (EMAEM) method was employed to study the 3D fractional Wazwaz-Benjamin-Bona-Mahony equation (WBBM), resulting in new sets of solutions. These solutions include kink and anti kink, periodic and doubly periodic, bell shaped, trigonometric functional solutions, hyperbolic solutions, singular kink, rational solutions, and combined soliton like solutions, which were graphically represented with detailed behavior of physical structure of solutions.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Mostafa M. A. Khater et al.
Summary: This study examines semi-analytical and numerical solutions of the time-fractional nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation using five latest numerical schemes. The model's solution represents the proliferation of a favored gene, and moving waves are pursued by nonlinear interaction. The obtained numerical solutions' consistency is examined through measuring the absolute error between the exact and numerical solutions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Applied
Mostafa M. A. Khater
Summary: In this paper, the generalized Jacobi elliptical functional and modified Khater methods are employed to find various wave solutions of the Ostrovsky equation, which show persistent and dominant features of localized wave packets. Multiple distinct solutions are obtained through the computational schemes, and the accuracy of the solutions is examined through a comparison with previously obtained results.
MODERN PHYSICS LETTERS B
(2021)
Article
Nanoscience & Nanotechnology
Mostafa M. A. Khater et al.
Summary: This paper investigates the analytical solutions of the perturbed nonlinear Schrodinger equation using the modified Khater method, obtaining various forms of solutions for the model. The model studied is significant in quantum fields as it describes the wave function of a quantum-mechanical system, with the physical characteristics of some solutions explained through contour plots. The novelty of the study is demonstrated by showing the consistency between the obtained solutions and those in previously published papers.
Article
Materials Science, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: This manuscript investigates the analytical and semi-analytical solutions of the nonlinear phi-four equation, which can be used to study quantum effects and explain phenomena in quantum physics.
RESULTS IN PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Usman Younas et al.
Summary: This paper examines the propagation of waves through magneto-optic waveguides using the generalized vector nonlinear Schrodinger's equation (NLSE). Two types of nonlinearities are studied, and exact solutions including various types of soliton solutions are obtained using the extended Fan-sub equation (EFSE) method. The significance of this approach lies in its ability to provide all solutions in a concise and efficient manner, as well as its applicability to more complex phenomena with symbolic computations.
RESULTS IN PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: This study investigated computational solutions for the fractional mathematical system form of HIV-1 infection of CD4(+) T-cells using three recent analytical schemes and the Atangana-Baleanu fractional derivative. The model, affected by antiviral drug therapy, accurately predicts the evolution of dynamic population systems involving virus particles. Multiple novel solutions were obtained using modified Khater (MKhat), sech-tanh expansion (STE), and extended simplest equation (ESE) methods, with the stability of the solutions analyzed using the Hamiltonian system's characterizations and visual representations of variable relationships in two dimensions.
RESULTS IN PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: This study handles the nonlinear KFG equation using two computational schemes to construct novel wave solutions, verifying their accuracy through matching and error calculation. The physical characteristics of the solutions are explained using various plots, and the originality of the investigation is confirmed through comparison with previous solutions.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: This research focuses on studying the computational solutions of the modified BBM equation using the modified Khater method, investigating the stability property of the obtained solutions, and evaluating the initial and boundary conditions to find numerical solutions of the suggested model using B-spline collection schemes. The model describes the propagation of long waves in nonlinear dispersive media in optical illusions field, with four distinct types of sketches employed for better understanding the obtained solutions.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Physics, Multidisciplinary
Muhammad Bilal et al.
Summary: Nonlinear Schrodinger-type equations are important models emerging from various fields, and different soliton solutions have been obtained using multiple methods, categorized into various types. The reported results include 2D, 3D, and contour profiles for better comprehension of the physical phenomena, demonstrating the efficiency and value of the proposed techniques for constructing new solutions for nonlinear partial differential equations.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2021)
Article
Physics, Applied
Mostafa M. A. Khater et al.
Summary: This paper investigates the accuracy of stable analytical solutions for the nonlinear fractional nonlinear time-space telegraph equation using the trigonometric-quantic-B-spline method. The study focuses on obtaining initial and boundary conditions from the analytical solutions to facilitate the application of the numerical scheme. Additionally, the accuracy of the analytical solutions is examined through the properties of the Hamiltonian system.
MODERN PHYSICS LETTERS B
(2021)
Article
Physics, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: This paper investigates the numerical wave solutions of two fractional biomathematical and statistical physics models, the KPP equation and the Z equation, using generalized Riccati-expansion analytical scheme and Caputo-Fabrizio fractional derivative. It converts the fractional nonlinear evolution equation into an ordinary differential equation with an integer order to describe the transmission of a preferred allele, nonlinear interaction of moving waves, and the relative wave mode's amplitude dynamic. The findings are illustrated with several drawings in two dimensions and density plots.
Article
Physics, Multidisciplinary
Mostafa M. A. Khater et al.
European Physical Journal Plus
(2021)
Article
Materials Science, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: This manuscript explores the calculations and approximate solutions of complex nonlinear Fokas-Lenells equations using the generalized Khater method and the trigonometric quintic B-spline scheme. The obtained novel computing solutions are plotted in graphs to explain the dynamic behavior of short pulses in optical fibers. The constructed analytical solutions are used to evaluate initial and boundary conditions and apply numerical solutions to study the accuracy of the novel computational techniques, demonstrating the effectiveness and versatility of the methods in analyzing nonlinear evolution equations.
RESULTS IN PHYSICS
(2021)
Article
Materials Science, Multidisciplinary
Hadi Rezazadeh et al.
Summary: This work studies the optical soliton solutions of the generalized non-autonomous NLSE using the new Kudryashov's method, considering three interesting non-Kerr laws. The proposed method is an efficient, reliable, and simple approach for computing new solutions to various kinds of NLPDEs in applied sciences and engineering.
RESULTS IN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: This paper investigates the analytical and semi-analytical solutions of the generalized CBS equation, demonstrating the dynamic behavior of soliton wave solutions in plasma. The method used shows effectiveness in various nonlinear evolution equations.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2021)
Article
Mathematics, Applied
Muhammad Bilal et al.
Summary: This research successfully discusses the exact soliton solutions to the double-chain model of deoxyribonucleic acid using new mathematical methods, which play an important role in biology. Some solutions are exemplified graphically to understand the physical meaning of the DNA model. The results show extremely rich exact wave structures of biological relevance.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Physics, Applied
Mostafa M. A. Khater
Summary: The research paper employs the trigonometric quintic B-spline scheme to investigate the numerical solution of Zakharov's nonlinear dimensional equation, exploring the connection between high-frequency Langmuir and low-frequency ion-acoustic waves with various applications. Different computational schemes have been utilized to study the model's moving wave solution, with innovative solutions established to determine suitable conditions for implementing multiple numerical schemes. The precision of the collected analytical solutions is analyzed using the trigonometric quintic B-spline method, and distinct drawings are provided to illustrate the accuracy of the numerical and computational solutions.
MODERN PHYSICS LETTERS B
(2021)
Article
Physics, Applied
Mostafa M. A. Khater
Summary: This paper investigates the solitary wave solutions of the complex perturbed Gerdjikov-Ivanov equation using the extended simplest equation and modified Khater methods. The physical characterization of optical soliton waves in mitigating internet bottlenecks is described, with the results demonstrated through various plots. The novelty of the obtained results is shown through comparison with previously obtained solutions, and the performance of computational applied schemes is tested for handling nonlinear evolution equations effectively.
MODERN PHYSICS LETTERS B
(2021)
Article
Physics, Applied
Mostafa M. A. Khater
Summary: This paper investigates the dynamical behavior of high-frequency waves in the relaxation medium using the Vakhnenko-Parkes and modified Khater methods, resulting in numerous novel solitary wave solutions and demonstrating the accuracy of solutions. The methods' performance is shown to be effective, direct, easy, and beneficial for studying various nonlinear evolution equations.
MODERN PHYSICS LETTERS B
(2021)
Article
Engineering, Electrical & Electronic
Muhammad Bilal et al.
Summary: In this research, various nonlinear dynamical optical soliton structures were extracted using three efficient mathematical tools, including specifically known solitary wave solutions, as well as securing singular periodic wave solutions with unknown parameters. The solutions were verified using Mathematica and modulation instability analysis for the given nonlinear Schrodinger model was conducted. The theoretical outcomes revealed immensely rich structures of optical soliton solutions.
OPTICAL AND QUANTUM ELECTRONICS
(2021)
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Mathematics
Sayyedeh Narges Hajiseyedazizi et al.
Summary: This paper investigates the existence of solutions for singular fractional q-integro-differential equations using the standard Caputo fractional q-derivative. The research focuses on compact mapping and the Lebesgue dominated theorem to find solutions and prove main results in the context of completely continuous functions. Examples involving graphs, tables, and algorithms are presented to illustrate the theoretical findings.
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Engineering, Marine
Asghar Ali et al.
Summary: The authors employed three novel methods to construct traveling wave solutions of the system of shallow water wave equations and modified Benjamin-Bona-Mahony equation, showing that these methods are more powerful tools for nonlinear wave equations.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2021)
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Physics, Fluids & Plasmas
Chen Yue et al.
Summary: This research focuses on the analytical solutions of fractional Hirota's solutions-Satsuma (HS) equations, converting the fractional system into an integer-order system using conformable fractional derivatives. Novel solutions for the model are constructed using the extended simplest equation (ESE) and modified Kudryashov (MKud) methods, with the accuracy of the solutions investigated through computational methods. The solutions are further explored through various sketches to demonstrate the novel properties of the model.
Article
Mathematics, Applied
Mostafa M. A. Khater et al.
Summary: In this manuscript, two recent numerical schemes were used to evaluate the approximate solutions of the nonlinear Klein-Gordon-Zakharov model, depicting the interaction between Langmuir wave and ion-acoustic wave in high-frequency plasma. Comparison between the solutions obtained in this study and those in previous research showed the accuracy of seven recent numerical schemes and their alignment with the considered model. The novelty, originality, and accuracy of the research paper were demonstrated through comparing the obtained numerical solutions with previously derived solutions.
Article
Physics, Multidisciplinary
Mostafa M. A. Khater et al.
Summary: In this manuscript, the computational solutions of the nonlinear Klein-Gordon-Zakharov (KGZ) model are scrutinized through a new generalized analytical scheme, demonstrating various physical and dynamical attitudes. The capabilities for managing a class of nonlinear evolution equations of the new generalized method are assessed, and the stability property of the obtained solutions is checked using the characteristics of the Hamiltonian system.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
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Mostafa M. A. Khater et al.
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