Related papers: On the Bj\"orling problem for Born-Infeld solitons
We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.
We obtain some equations for Hamiltonian-minimal Lagrangian surfaces in CP^2 and give their particular solutions in the case of tori.
The fact that minimal surfaces in the four-dimensional Euclidean space admit natural parameters implies that any minimal surface is determined uniquely up to a motion by two curvature functions, satisfying a system of two PDE's (the system…
We give an immersion formula, the Sym-Bobenko formula, for minimal surfaces in the 3-dimensional Heisenberg space. Such a formula can be used to give a generalized Weierstrass type representation and construct explicit examples of minimal…
In this paper we introduce the $(n+2)$-dimensional Born-Infeld action with a dual field strength $\tilde{H}$. We compute the field equation by using Schur polynomials and give a soliton solution.
We study an elliptic equation related to the Moser-Trudinger inequality on a compact Riemann surface $(S,g)$, $$ \Delta_g u+\lambda \Biggl(ue^{u^2}-{1\over |S|} \int_S ue^{u^2} dv_g\Biggl)=0,\quad\text{in $S$},\qquad \int_S u\,dv_g=0, $$…
In this paper, we completely classify conformal solitons on pseudo-Riemannian hypersurfaces in pseudo-Euclidean spaces arisen from the position vector field. In particular, the classification of Yamabe solitons on pseudo-Riemannian…
In this article it is shown that the fundamental equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of curved space-time. We further generalize the results to…
This paper studies the problem of finding a three-dimensional solenoidal vector field such that both the vector field and its curl are tangential to a given family of toroidal surfaces. We show that this question can be translated into the…
In this paper we study solitons invariant with respect to the flow generated by a complete Killing vector field in a ambient Riemannian manifold. A special case occurs when the ambient manifold is the Riemannian product $(\mathbb{R} \times…
Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.
The electrostatic configurations of the Born-Infeld field in the 2-dimensional Euclidean plane are obtained by means of a non-analytical complex mapping which captures the structure of equipotential and field lines. The electrostatic field…
One of the most important tasks in mathematics and physics is to connect differential geometry and nonlinear differential equations. In the study of nonlinear optics, integrable nonlinear differential equations such as the nonlinear…
New isoperimetric inequalities for lower order eigenvalues of the Laplacian on closed hypersurfaces, of the biharmonic Steklov problems and of the Wentzell-Laplace on bounded domains in a Euclidean space are proven. Some open questions for…
We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean…
We consider the inverse scattering transform for the nonlinear Schr\"{o}dinger equation in laboratory coordinates (NLSLab equation) with nonzero boundary conditions (NZBCs) at infinity. In order to better deal with the scattering problem of…
We obtain the characteristic equation for the nonlinear Born-Infeld electrodynamics. This equation has the form of the characteristic equation for the linear electrodynamics in some effective Riemann space. The effective metric include the…
We describe the equations of motion of elastodynamic bounded bodies in 3-space, and their linearizations at a stationary point. Using the latter as an approximation to model small motions, we develop a scheme to find numerical solutions of…
We consider the family of the Bour's minimal surfaces in Euclidean 3-space, and compute their classes, degrees and integral free representations.
We get a continuous one-parameter new family of embedded minimal surfaces, of which the period problems are two-dimensional. Moreover, one proves that it has Scherk second surface and Hoffman-Wohlgemuth example as limit-members.