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Advances in Mathematical Physics
Scopus
ISSN 1687-9120 · Wiley · 1,569 articles in the index
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Journal Article
Combining Symmetries and Helmholtz’s Conditions to Construct Lagrangians
We present new relations derived from Noether’s identity that reveal the compatibility between the components of the Hessian matrix of the Lagrangian, the infinitesimal symmetry transformation of the configuration variables and time, and a constant of motion. Using these relations, we develop two…
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Journal Article
The Novel Numerical Solutions for Time-Fractional Fishers Equation
A new method for solving time-fractional partial differential equations (TFPDEs) is proposed in the paper. It is known as the fractional Kamal transform decomposition method (FKTDM). TFPDEs are approximated using the FKTDM. The FKTDM is particularly effective for solving various types of fractional…
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Journal Article
Constructing Traveling Wave Solutions via a Generalized Expansion Method for Nonlinear Evolution Equations Possessing Variable Coefficients
In this article, a highly generalized way of studying nonlinear evolution equations (NLEEs) with time-dependent variable coefficients is provided. The innovative exact solutions of the Kadomtsev–Petviashvili (KP) equation and the modified Korteweg–de Vries (mKdV) equation with temporal variable…
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Journal Article
Dynamical Optical Structure Solutions of the Time-Fractional Chen-Lee-Liu Equation
In this article, we utilize the conformable fractional (CF) derivative to investigate the analytically innovative soliton solutions for the time-fractional nonlinear perturbed Chen-Lee-Liu (CLL) equation in optical fibers. An essential governing equation in nonlinear optics, the perturbed CLL model…
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Journal Article
Generalized Synchronization of Complex Neuron Networks in Driver-Response Configuration for Chaotic Processes
This paper presents the generalized synchronization of neuronal networks in a unidirectionally coupled drive-response system with interconnected nodes exhibiting chaotic behavior. The study focuses on the synchronization of the Hindmarsh–Rose (HR) neuronal mathematical model through connections…
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Journal Article
Regularization by Global DGMRES Method for Ill-Posed Matrix Equation AXB=G
In this article, we deal with the solution of the linear, large-size, and ill-posed matrix equation AXB=G, whose matrix G is contaminated with noise. We apply Tikhonov regularization in combination with the Gl-DGMRES method to mitigate the effect of noise. Our implementation is performed on…
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Journal Article
Phase-Lag Integro-Partial Differential Equation: Local and Nonlocal Solutions
Nonlocal information, such as material deformation, genetic genes, or the history of the disease, are essential as they provide us with additional details that increase the numerical solution’s accuracy. With the help of the phase delay, we may also predict the future of the phenomena we are…
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Journal Article
Kudryashov Expansion Method Applied to Fisher Mathematical Model
We obtain new computational soliton solutions characterized by topological, rational, exponential, trigonometric, and hyperbolic functions for the Fisher equation. Using a good strategy, the Kudryashov expansion method is used to find different dynamical wave structures of soliton solutions within…
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Journal Article
Diverse Soliton Structures of Induced Curves in the Integrable Coupled Kuralay Equation
This study explores the integrable coupled Kuralay equation, which is widely utilized to study the motion of induced curves. In fields such as ferromagnetic materials, nonlinear optics, and optical fibers, soliton solutions of the Kuralay equation have emerged as significant recent developments…
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Journal Article
Torsional Vibration of a Nanobeam Under Magnetic Load and Surrounded With Torsional Spring, Based on the Modified Couple Stress Theory Using Power Series Method
This paper is concerned with the torsional vibration of the nanobeam under a longitudinal magnetic field and surrounded by a torsional spring. The small size effect is taken into account by considering the modified couple stress theory of elasticity for continuum mechanics, and the power series…
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Journal Article
Hopf Bifurcation Analysis and Matched Asymptotics for a Bi-Stable Flame Propagation Model
In this article, we consider a model for flame propagation dynamics influenced by both temperature and pressure. The model is based on nonlinear diffusion and incorporates elements from porous structure theory within the framework of partial differential equations. Initially, Hopf bifurcation…
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Journal Article
Numerical Investigation of Unsteady Magnetohydrodynamic Casson Hybrid Nanofluid Flow Through a Stenosed Artery: Effects of Viscous Dissipation, Joule Heating, Thermal Radiation and Chemical Reaction
This study numerically investigates the unsteady magnetohydrodynamic (MHD) flow of a blood-based Casson hybrid nanofluid containing gold (Au) and iron oxide (Fe3O4) nanoparticles, flowing through a stenosed artery. The viscous dissipation, Joule heating, thermal radiation and porosity effects…
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Journal Article
Optical Soliton Solutions and Modulation Instability of the Higher-Order Complex Cubic-Quintic Ginzburg–Landau Equation
The propagation of ultrashort optical pulses in nonlinear dissipative media is investigated through a generalized higher-order cubic–quintic complex Ginzburg–Landau equation (HG CQ-CGLE) incorporating third-order dispersion (TOD), fourth-order dispersion (FOD), self-steepening (SS), and intrapulse…
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Journal Article
Exact Solution for Fuzzy-Informed Nonlinear Bi-Hamiltonian Camassa–Holm Model for Shallow-Water Waves
In this paper, the analytical properties of the fuzzy Camassa–Holm equation (FCHE) with a sophisticated model are investigated and used to describe nonlinear wave phenomena under fuzzy conditions. The fuzzy set theory is employed to incorporate uncertainty into physical parameters in shallow water…
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Journal Article
Bifurcation Analysis and Qualitative Dynamics of the Time-Delayed Holling–Tanner Prey-Predator Model
In this study, we work on a Holling–Tanner prey-predator (HTPP) model by incorporating the impact of predator cannibalism and later introducing a delay in prey growth. We first examine its behavior without delay: we identify equilibrium points, describe their stability, and explain when the system…
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Journal Article
Independence Polynomial-Based Approach for Fredholm–Volterra Integro-Differential Problems of High Order
A numerical collocation approach employing independence polynomials of paths is formulated to approximate the solutions of high-order linear Fredholm–Volterra integro-differential problems under mixed conditions. The proposed approach transforms the given equation and conditions into a matrix form…
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Journal Article
Exact Soliton Solutions and Complex Dynamical Analysis of the Nonlinear Model Arising in Mathematical Physics
This study investigates the 1+1-dimensional Sharma–Tasso–Olver–Burgers (STOB) equation, a nonlinear model arising in mathematical physics. The modified F-expansion method is employed to derive a variety of exact soliton solutions, including trigonometric, hyperbolic, singular, periodic, and…
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Journal Article
A Novel Numerical Algorithm for Singularly Perturbed Parabolic Problems With Discontinuous Convection Coefficient and Source Terms
MSC2020 Classification: 35B25, 65M06, 65N12
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Journal Article
A Physics-Informed Neural Networks for Solving 2D Frequency-Domain Electromagnetic Waves in the Differential Form of Maxwell’s Equations
This article investigates the application of physics-informed neural networks (PINNs) for solving two-dimensional (2D) frequency-domain Maxwell’s equations in complex geometries, including rectangular, circular, annular, and eccentric circular domains. The problem is reformulated into a system of…
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