Abstract
We study the existence and uniqueness of solutions to the vector field Peierls–Nabarro (PN) model for curved dislocations in a transversely isotropic medium. Under suitable assumptions for the misfit potential on the slip plane, we reduce the 3D PN model to a nonlocal scalar Ginzburg–Landau equation. For a particular range of elastic coefficients, the nonlocal scalar equation with explicit nonlocal positive kernel is derived. We prove that any stable steady solution has a one-dimensional profile. As a result, we obtain that solutions to the scalar equation, as well as the original 3D system, are characterized as a one-parameter family of straight dislocations. This paper generalizes results found previously for the full isotropic case to an anisotropic setting.
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