Related papers: On the Bj\"orling problem for Born-Infeld solitons
In this semi-expository article, we study Born-Infeld soliton surfaces as zero mean curvature surfaces and derive conformal parameters for them. Then we present two approaches to solve the Bj\"orling problem for such surfaces, one of them…
In this paper we will show the existence and uniqueness of the solution of the Bj\"orling problem for minimal surfaces in a 3-dimensional Lorentzian Lie group.
We show that a Born-Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. We also obtain some exact solutions of the…
We introduce a new approach to the study of timelike minimal surfaces in the Lorentz-Minkowski space through a split-complex representation formula for this kind of surface. As applications, we solve the Bj\"orling problem for timelike…
We prove existence and uniqueness of the solution of the Bj\"orling problem for minimal surfaces in a three-dimensional Lie group.
In this paper, we discuss a one parameter family of complex Born-Infeld solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B-I equation from a given complex solution of…
The Bj\"orling problem amounts to the construction of a minimal surface from a real-analytic curve with a given real-analytic normal vector field. We approximate that solution locally by discrete minimal surfaces as special discrete…
The non-linear second order Born-Infeld equation is reduced to a simpler first order complex equation, which can be trivially solved for the coordinates as functions of the field. Each solution is determined by the choice of a holomorphic…
We study standing-wave solutions of Born-Infeld electrodynamics, with nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the…
In this paper we solve the Bj\"orling problem for the class of immersed surfaces in $\mathbb{R}^3$ whose mean curvature is given as an analytic function depending on its Gauss map. As an application, we prove the existence of surfaces with…
The classical Bj\"orling problem is to find the minimal surface containing a given real analytic curve with tangent planes prescribed along the curve. We consider the generalization of this problem to non-minimal constant mean curvature…
We develop a new method to construct explicit, regular minimal surfaces in Euclidean space that are defined on the entire complex plane with controlled geometry. More precisely we show that for a large class of planar curves $(x(t), y(t))$…
We study the Einstein-Klein-Gordon system coupled to the Born-Infeld electrodynamics. We explore the solution space of a static spherically symmetric, complex scalar field minimally coupled to both gravitational and electromagnetic fields.…
This paper is devoted to a study of the connection between the immersion functions of two-dimensional surfaces in Euclidean or hyperbolic spaces and classical orthogonal polynomials. After a brief description of the soliton surfaces…
The main objective of this paper is to derive the Enneper-Weierstrass representation of minimal surfaces in $\mathbb{E}^3$ using the soliton surface approach. We exploit the Bryant-type representation of conformally parametrized surfaces in…
Classical version of Born-Infeld electrodynamics is recalled and its most important properties discussed. Then we analyze possible abelian and non-abelian generalizations of this theory, and show how certain soliton-like configurations can…
We study minimal graphs in the homogeneous Riemannian 3-manifold $\widetilde{PSL_2(\mathbb{R})}$ and we give examples of invariant surfaces. We derive a gradient estimate for solutions of the minimal surface equation in this space and…
We use the method of higher order linearization to study an inverse boundary value problem for the minimal surface equation on a Riemannian manifold $(\mathbb{R}^n,g)$, where the metric $g$ is conformally Euclidean. In particular we show…
The singular Bj\" orling problem and its solution for timelike minimal surfaces is a well-known result in minimal surface theory. In this article, we give a different proof of this theorem using split-harmonic maps. This is motivated by a…
This paper gives, in generic situations, a complete classification of ruled minimal surfaces in pseudo-Euclidean space with arbitrary index. In addition, we discuss the condition for ruled minimal surfaces to exist, and give a…