Article
Astronomy & Astrophysics
Yisong Yang
Summary: We study the equations of motion for static dyonic matters using nonlinear electrodynamics of the Born-Infeld theory type. Exact finite-energy solutions are obtained in the quadratic and logarithmic nonlinearity cases, which lead to dyonically charged black holes with relegated curvature singularities. We demonstrate that the dyonic solutions restore electromagnetic symmetry and resolve a density-pressure inconsistency issue exhibited by the original Born-Infeld model.
Article
Astronomy & Astrophysics
Nora Breton, Claus Laemmerzahl, Alfredo Macias
Summary: We formulate the Einstein-Euler-Heisenberg system of field equations with a cosmological constant for type -D metrics using the null tetrad formalism. We find all type -D solutions to these equations, including the generalized versions of Bertotti-Robinson, Reissner-Nordstrom, Newman-Unti-Tamburino-B (NUT-B)(+), and Kerr-Newman solutions. Additionally, we demonstrate that the (static) C-metric is not compatible with the Euler-Heisenberg electrodynamics.
Article
Astronomy & Astrophysics
Daniel Amaro, Alfredo Macias
Summary: In this study, we construct the exact lens equation for the electrically charged static black hole spacetime of the Einstein-Euler-Heisenberg theory. We compare this equation with the thin-lens equations and the corresponding equations for the Reissner-Nordstrom solution. The shadow of the black hole, the angular-diameter distance to the sources, and the time delay of arrival of the images are also calculated and discussed.
Article
Mathematics, Applied
J. C. Ndogmo
Summary: An extension of a new method of group classification was applied to a family of nonlinear wave equations labelled by two arbitrary functions. The efficiency of the proposed method for group classification, called the method of indeterminates, was confirmed by the obtained results. A model equation from the classified family of fourth order Lagrange equations was identified. Travelling wave solutions of this equation were found through variational symmetry operators, followed by reduction into a second order ordinary differential equation. Multi-soliton solutions and other exact solutions were also discovered using Lie group and Hirota methods. The general action of the full symmetry group on any given solution was provided, and some remarkable facts on Lagrange equations arising from the study were outlined.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics
Xiaoming Wang, Shehbaz Ahmad Javed, Abdul Majeed, Mohsin Kamran, Muhammad Abbas
Summary: In this article, an analytical technique based on the unified method is applied to investigate the exact solutions of nonlinear homogeneous evolution partial differential equations. By reducing these partial differential equations to ordinary differential equations using different traveling wave transformations, exact solutions in rational and polynomial forms are obtained. The obtained solutions are presented in 2D and 3D graphics to study their behavior, and the results show that the unified method is a suitable approach for handling nonlinear homogeneous evolution equations.
Article
Physics, Multidisciplinary
Stuart T. Johnston, Matthew J. Simpson
Summary: This paper presents exact sharp-fronted solutions to a model of degenerate nonlinear diffusion on a growing domain, addressing both the lack of understanding on the relationship between model parameters and solution features in numerical solutions and the inability of linear diffusion to capture sharp fronts observed in experiments.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Qiuyan Zhang, Yuqian Zhou, Jibin Li
Summary: The nonlinear Schrodinger equation with nonlinear dispersion is investigated, and the bifurcation-theoretic method of planar dynamical systems is used to obtain various exact solutions for this system.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Engineering, Electrical & Electronic
Yongming Xu, Yuqiang Feng, Jun Jiang
Summary: In this study, the resonant nonlinear Schrodinger equation with dual-power law nonlinearity is extended to the fractional case, leading to the derivation of novel exact solutions. These solutions, including bright, dark, and singular solitons, are of great importance in addressing specific optical issues.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Mathematics, Applied
Pietro d'Avenia, Marco G. Ghimenti
Summary: In this paper, we prove the existence of multiple solutions for a given system of equations under certain conditions. We also provide a characterization of low energy solutions.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Andrei D. Polyanin, Vsevolod G. Sorokin
Summary: The study introduces new indirect methods for constructing exact solutions of nonlinear PDEs with delay, including reaction-diffusion equations and wave-type equations. The proposed methods can generate exact solutions for equations with different types of delays, and can also be applied to nonlinear systems of coupled delay PDEs and higher-order delay PDEs. Additionally, the equations and their exact solutions investigated in the study can serve as test problems for evaluating the accuracy of various numerical and approximate analytical methods for solving nonlinear initial-boundary value problems for delay PDEs.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Astronomy & Astrophysics
Mario Pitschmann
Summary: The exact analytical solutions to the symmetron field theory equations with one or two-mirror system in both vacuum and matter cases have been derived. These solutions, expressed in terms of Jacobi elliptic functions, can be applied to various experiments such as qBOUNCE and neutron interferometry. The analysis helps to broaden the understanding of symmetron properties and mechanisms by considering its phase in both vacuum and matter.
Article
Multidisciplinary Sciences
Seham Ayesh Allahyani, Hamood Ur Rehman, Aziz Ullah Awan, ElSayed M. Tag-ElDin, Mahmood Ul Hassan
Summary: This article aims to obtain new soliton solutions for the Gilson-Pickering equation using Sardar's subequation method and Jacobi elliptic function method. The solutions obtained are unique, remarkable, and significant for readers. Mathematica 11 software is used to derive and demonstrate the graphical representations of the solutions.
Article
Mathematics, Applied
Andrei D. Polyanin, Vsevolod G. Sorokin
Summary: A new method is proposed for constructing exact solutions of nonlinear delay PDEs using simpler auxiliary PDEs without delay. The method is demonstrated on nonlinear reaction-diffusion and wave-type equations with delay, resulting in new generalized traveling-wave solutions and functional separable solutions. The results can be used to verify and evaluate the accuracy of numerical and approximate analytical methods for solving corresponding nonlinear initial-boundary value problems with delay.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Materials Science, Multidisciplinary
U. Younas, M. Younis, Aly R. Seadawy, S. T. R. Rizvi, Saad Althobaiti, Samy Sayed
Summary: This article focuses on extracting diverse exact solutions for the CTFMNLSE, which describes water wave propagation in ocean engineering. Trigonometric, hyperbolic, and exponential function solutions are extracted, along with special wave solutions like shock waves, singular solutions, and complex solitons. The GERFM method is used to explain soliton dynamics, and constraint conditions for solution existence are discussed, as well as the recovery of singular periodic wave solutions. These solutions are beneficial for interpreting wave propagation studies and for numerical and experimental verifications in ocean engineering.
RESULTS IN PHYSICS
(2021)
Article
Mathematics
Andrei D. Polyanin, Vsevolod G. Sorokin
Summary: This study focuses on nonlinear pantograph-type reaction-diffusion PDEs, examining equations with scaling parameters and exact solutions. The analysis includes examples with proportional delay, various types of solutions, and discussions on the principle of analogy for constructing solutions. The research also delves into more complex functional differential equations with varying delay, highlighting the potential for evaluating numerical methods and formulating test problems.
