Related papers: Exact solutions for U(1) globally invariant membra…
The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one…
Nonlinear equations of $p$-branes in $D=(2p+1)$-dimensional Minkowski space are discussed. Presented are new exact solutions for a set of spinning $p$-branes with $p=2,3,...,(D-1)/2$ and the Abelian symmetries $U(1)\times U(1)\times...…
New classes of exact M(em)brane solutions in M+2 dimensional Minkowski space are presented (some describing non-trivial topology changes, while others explicitly avoid finite-time singularity formation)
We introduce a particular embedding of seven dimensional self-duality membrane equations in C^3\times R which breaks G_2 invariance down to SU(3). The world-volume membrane instantons define SU(3) special lagrangian submanifolds of C^3. We…
We find a new family of exact solutions in membrane theory, representing toroidal membranes spinning in several planes. They have energy square proportional to the sum of the different angular momenta, generalizing Regge-type string…
Exact solvability of brane equations is studied, and a new $U(1)\times U(1)\times... \times U(1)$ invariant anzats for the solution of $p$-brane equations in $D=(2p+1)$-dimensional Minkowski space is proposed. The reduction of the $p$-brane…
A formulation of U(1) - symmetric classical membrane motions (preserving one rotational symmetry) is given, and reductions to systems of ODE's, as well as some ideas concerning singularities and integrability.
The exact quantum integrability problem of the membrane is investigated. It is found that the spherical membrane moving in flat target spacetime backgrounds is an exact quantum integrable system for a particular class of solutions of the…
This paper is devoted to the study of the singularity phenomenon of timelike extremal hypersurfaces in Minkowski spacetime $\mathbb{R}^{1+3}$. We find that there are two explicit lightlike self-similar solutions to a graph representation of…
We study spiky configurations of membranes in the SO(d)xSU(N) invariant matrix models. A class of exact solutions (analogous to plane-waves) of the corresponding Schroedinger equation for an arbitrary N is discussed. If the large N limit is…
A set of N three component unit scalar fields in (3+1) Minkowski space-time is investigated. The highly nonlinear coupling between them is chosen to omit the scaling instabilities. The multi-soliton static configurations with arbitrary Hopf…
We obtain exact rotating membrane solutions and explicit expressions for the conserved charges on a manifold with exactly known metric of G_2 holonomy in M-theory, with four dimensional N=1 field theory dual. After that, we investigate…
Noncommutative U(1) gauge theory in 4-dimensions is shown to be equivalent in some scaling limit to an ordinary non-linear sigma model in 2-dimensions . The model in this regime is solvable and the corresponding exact beta function is…
We find general, time-dependent solutions produced by open string sources carrying no momentum flow in 2+1 dimensional gravity. The local Poincar\'e group elements associated with these solutions and the coordinate transformations that…
We perform a systematic search for N=1 Minkowski vacua of type II string theories on compact six-dimensional parallelizable nil- and solvmanifolds (quotients of six-dimensional nilpotent and solvable groups, respectively). Some of these…
We consider the the n-dimensional generalisation of the nonholonomic Veselova problem. We derive the reduced equations of motion in terms of the mass tensor of the body and determine some general properties of the dynamics. In particular we…
In this paper, we prove the nonlinear stability in exponential time of Minkowki space-time with a translation space-like Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein…
In the lightcone frame, where the supermembrane theory and the Matrix model are strikingly similar, the equations of motion admit an elegant complexification in even dimensional spaces. Although the explicit rotational symmetry of the…
We show that the leading-order term in the late-time asymptotics of solutions to the linear wave equation on radially symmetric stationary perturbations of $(2 + 1)$-dimensional Minkowski space is proportional to $u^{-1/2}v^{-1/2}$ (which…
There is a few results about the global stability of nontrivial solutions to quasilinear wave equations. In this paper we are concerned with the uniqueness and stability of traveling waves to the time-like extremal hypersurface in Minkowski…