  Charge density waves (CDW) profoundly affect the electronic properties of
materials and have an intricate interplay with other collective states, like
superconductivity and magnetism. The well-known macroscopic Ginzburg-Landau
theory stands out as a theoretical method for describing CDW phenomenology
without requiring a microscopic description. In particular, it has been
instrumental in understanding the emergence of domain structures in several CDW
compounds, as well as the influence of critical fluctuations and the evolution
towards or across lock-in transitions. In this context, McMillan's foundational
work introduced discommensurations as the objects mediating the transition from
commensurate to incommensurate CDW, through an intermediate nearly commensurate
phase characterised by an ordered array of phase slips. Here, we extend the
simplified, effectively one-dimensional, setting of the original model to a
fully two-dimensional analysis. We find exact and numerical solutions for
several types of discommensuration patterns and provide a framework for
consistently describing multi-component CDW embedded in quasi-two-dimensional
atomic lattices.
