Complex scalar fields in one dimension with fourfold phase anisotropy: Solitary-wave solutions

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Abstract
We present solitary-wave solutions to a set of coupled nonlinear wave equations resulting from a model Lagrangian for a complex scalar (two-component) field in one space and one time dimension in the presence of fourfold phase anisotropy in the potential-energy density. We find two classes of solutions which correspond to 90° and 180° phase rotation, respectively. The 180° solution is found to bifurcate into two 90° solutions as the anisotropy magnitude is decreased past a special value. These results have application to commensurability-pinned one-dimensional charge-density-wave condensates and anisotropic ferromagnetic domain walls.