Superconducting circuits are a promising platform for quantum engineering. They have many applications ranging from amplifiers and detectors to quantum computers and quantum metrological standards. Superconducting circuits are also used in fundamental science, as they can simulate paradigmatic models of quantum many-body physics and quantum electrodynamics. One example of fundamental effects is lasing that has been observed for a small nonlinear driven quantum system (a voltage-biased Josephson junction) coupled to a microwave photonic bath (a multi-mode superconducting resonator). Another experiment showed that a similar system could also end up in a thermal rather than coherent state. The task now is to develop a theory which could describe the transition between coherent and thermal states of the resonator. On the semiclassical level, we have to describe a transition between regular and chaotic motion of a complex dynamical system. On the quantum level, we face the problem of thermalization or its absence in a driven-dissipative quantum many-body system. The first step, which is the subject of this internship, will be to construct a classical coherent lasing solution for a lambda/4 resonator. This work will involve analytical and numerical calculations.