We demonstrate that the reconstruction of the Au(l 11) surface can be interpreted in terms of a new type of misfit dislocations, namely, double-sine-Gordon-type dislocations. First, we motivate the applicability of this class of solitons to the reconstruction problem. Second, we describe the procedure we have used to construct the model unit cell containing the double-sine-Gordon quasi one-dimensional dislocations. Finally, comparison with experimental He-scattering results is established by computation of the corresponding diffraction pattern using a hard corrugated wall and the eikonal approximation.

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We present a complete Hamiltonian treatment of a kink with an internal degree of freedom, namely the double sine-Gordon (DSG) kink. In this formalism we assign two canonical coordinates and their associated momenta to describe the motion of the center of mass of the DSG kink and the relative motion of its two subkinks. We show that the canonical coordinate representing the separation of the two subkinks describes a nonlinear oscillatory degree of freedom. Consequently, the DSG kink behaves like a "molecule" (4~kink) comprised of two "atoms" (each of a single 2~kink) held together by a nonlinear potential. As an application of our formalism, we obtain the solutions for the nonlinear internal motion of the DSG in the absence of the radiation field.

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