Explicit self-similiar singularity of Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation

Abstract

This paper studies the self-similar singularity phenomenon of zero mean curvature equation including Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation which arises in string theory and geometric minimal surfaces theory. We show that there exist new explicit self-similar solutions for Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation in Minkowski space $R^{1+3}$ with respect to the radially symmetric case.

9 pages. arXiv admin note: text overlap with arXiv:1708.06289

References in corpus (3)

• Testing Born-Infeld electrodynamics in waveguides
• Singularities in string theory
• Approximated solutions to Born-Infeld dynamics

Cited by in corpus (3)

• Dynamical behavior near explicit self-similar blow up solutions for the Born-Infeld equation
• On the explicit blowup solutions for 3D incompressible Magnetohydrodynamics equations
• Finite time blowup explicit solution for 3D incompressible Euler equations