Abstract
We study a system of elliptic equations from the Abelian Born–Infeld system coupled with the Einstein equations under the boundary condition of symmetric vacuum (nontopological type). When the total string number satisfies 1 ⩽ N < 1/4π G, where G is the gravitational constant, we construct a family of solutions to the system. The qualitative properties of the solutions are quite different from the solutions with the boundary condition of broken vacuum symmetry.
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