Quasi-periodic relativistic strings in the Minkowski space ${\text{R}}^{1+n}$

Abstract

In this article we consider the motion of relativistic strings in the Minkowski space ${\text{R}}^{1+n}$. Those surfaces are known as a timelike minimal surface, and described by a system with $n$ nonlinear wave equations of Born-Infeld type. By constructing a suitable Nash-Moser iteration scheme, we prove that the $n$-dimensional relativistic strings can admit a more generalized time quasi-periodic motion in ${\text{R}}^{1+n}$. Moreover, those time quasi-periodic solutions are also timelike solutions.

19 pages

References in corpus (2)

• On smoothness of timelike maximal cylinders in three dimensional vacuum spacetimes
• Some geometric PDEs related to hydrodynamics and electrodynamics