# Tag Info

3

Joshphysics has already given a nice answer showing that in 2+1 dimensional Einstein gravity any metric is locally equivalent to a metric of constant curvature. As dilaton mentioned in a comment this in particular means that there are no local excitations. The updated question also asks about 1+1 dimensions. In this case the answer is even simpler: the 1+1 ...

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There is nothing "wrong" with the Einstein field equations in $2+1$ as indicated by the comments, but they do have interesting, significantly restricted behavior in $2+1$ dimensions. For example, the Wikipedia page referred to by Olof in the comments says that in $2+1$, every vacuum solution is locally either $\mathbb R^{2,1}$, $\mathrm{AdS_3}$, or ...

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Solitons are just nonlinear waves. They appear in almost any nonlinear system, similar to usual (linear) waves that characterize excitations in different systems (deformation waves, acoustic waves, electromagnetic waves). A distinguishing feature of a soliton is that it is localized in space. Usually, a soliton has a bell-shaped form (sometimes, this type is ...

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First, what is a difference between linear and nonlinear physical processes? If a deviation of a system from an equilibrium is small, then the system is said to be linear. Formally, in this case, the system is described by a linear equation. A simple example of a linear system is a pendulum that performs small oscillations near the equilibrium (vertical) ...

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