Related papers: Born-Infeld equations
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
The Bj\"orling problem and its solution is a well known result for minimal surfaces in Euclidean three-space. The minimal surface equation is similar to the Born-Infeld equation, which is naturally studied in physics. In this…
The method of solving of nonlinear Schr\"odinger equation is considered. Some examples of its applications are demonstrated.
We generalize Maxwell equations which describe the vacuum of quantum electrodynamics into the quantum form. This nontraditional approach is different from the widely used theory|-Quantum Electrodynamics. From another viewpoint, it could be…
The stationary axisymmetric spacetime coupled to nonlinear Born-Infeld electrodynamics is studied. The solution was derived by Plebanski et al (1984) and it is characterized by six free parameters: mass, NUT charge, electric and magnetic…
This is a brief introduction to the world of Noncommutative Algebra aimed at advanced undergraduate and beginning graduate students.
This letter is my comment about the opinion paper: Transdisciplinary electric power grid science (PNAS, 2013 - http://www.pnas.org/content/110/30/12159.full). [arXiv:1307.7305].
When B\"acklund transformations are applied repeatedly to any solution of the nonlinear equations describing electrodiffusion through a liquid junction separating two infinite well-stirred layers, they give rise to quantized ionic fluxes…
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
Series of short contributions that are part of Nobel Symposium 162 - Microfluidics arXiv:1712.08369.
We present basic results, known and new, on nontrivial solutions of periodic stationary nonlinear Schr\"odinger equations. We also sketch an application to nonlinear optics and discuss some open problems.
The electric potential and the electromagnetic field for a linearly accelerated Born-Infeld charged particle are obtained in an inertial frame by a method that can, in principle, be applied to any electromagnetic theory. The method is based…
This is an introductory article to the theory of multiple gaps.
Contents: 1 Frustrated quantum spin systems 1.1 The Pyrochlore checkerboard 1.2 Singlets in reflection symmetric spin systems 2 Wehrl entropy of Bloch coherent states 2.1 Conjectures of Wehrl and Lieb 2.2 Proof of Lieb's conjecture for low…
I compiled a list of articles on arXiv that deal with possible fundamental quantum nonlinearities or examine the origins of its linearity. The list extends til August 2004.
Using a new infinite-dimensional linking theorem, we obtained nontrivial solutions for strongly indefinite periodic Schr\"odinger equations with sign-changing nonlinearities.
In previous paper we have shown that there is a special kind of nonlinear electrodynamics - Curvilinear Wave Electrodynamics (CWED), whose equations are mathematically equivalent to the equations of quantum electrodynamics. The purpose of…
The Integration Theory of Linear Ordinary Differential Equation.
The summary of the Author's results on Bell inequalities and macroscopic entanglement.
The mechanism for the generation of a dipole moment due to an external field is presented for the Born-Infeld charged particle. The 'polarizability coefficient' is calculated: it is proportional to the third power of the characteristic…