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Nonlinear Dirac Equations [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2009
We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance.
Wei Khim Ng, Rajesh R. Parwani
doaj   +5 more sources

Newton-Krylov generalized minimal residual algorithm in solving nonlinear Volterra-Fredholm-Hammerstein integral equations [PDF]

Mathematics and Computational Sciences, 2021
In this paper, Galerkin and collocation methods based on shifted Legendre polynomials and spectral methods have been applied on nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations, these methods transfer the finding solution of a nonlinear ...
Ahmad Zavvartorbati
doaj   +1 more source

On convergence of explicit finite volume scheme for one-dimensional three-component two-phase flow model in porous media

Demonstratio Mathematica, 2021
In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir.
Mostefai Mohamed Lamine, Choucha Abdelbaki, Cherif Bahri   +2 more
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Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

Advances in Mathematical Physics, 2021
In this paper, the dynamical properties and the classification of single traveling wave solutions of the coupled nonlinear Schrödinger equations with variable coefficients are investigated by utilizing the bifurcation theory and the complete ...
Zhao Li, Peng Li, Tianyong Han
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Solving of some nonlinear ordinary differential equations in the form of power series

Физико-химические аспекты изучения кластеров, наноструктур и наноматериалов, 2022
In the current scientific literature, a variety of nonlinear ordinary differential equations are widely and successfully used to describe real processes in various fields of natural sciences: optics, elasticity theory, molecular physics, etc. For example,
I.N. Belyaeva, I.K. Kirichenko, N.N. Chekanova   +2 more
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On the Method of Transformations: Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations

Axioms, 2023
Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method.
Nikolay K. Vitanov
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On Removable Singularities of Solutions of Higher-Order Differential Inequalities

Advanced Nonlinear Studies, 2020
We obtain sufficient conditions for solutions of the mth-order differential ...
Kon’kov A. A., Shishkov A. E.
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Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations

Mathematics, 2023
Differential equations are useful mathematical tools for solving complex problems. Differential equations include ordinary and partial differential equations.
Liang Song, Shaodong Chen, Guoxin Wang
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Nonlinear Pauli Equation

Communications in Analysis and Mechanics, 2022
In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a ...
openaire   +2 more sources

Nonlinear Maxwell Equations [PDF]

Journal of Nonlinear Mathematical Physics, 1996
6 pages ...
openaire   +3 more sources