Phase transitions in general sine-Gordon equation

This bachelor's thesis delves into the Pokrovsky-Talapov model, exploring its implications in several physical processes. Of particular significance is its utilization in the quantum Hall effect. The paper comprehensively discusses the mathematical framework underlying this model, focusing on the conditions necessary for obtaining a soliton lattice and determining its energy density for different parameter values. Furthermore, the critical parameter value, the phase transition point of the system, and its dependence on the parameter are rigorously examined and derived within the context of this study.