  Statistical mechanics arguments and Madelung hydrodynamical presentation are
applied to the transport of magma in volcanic conduits. An effective wave
equation with logarithmic nonlinearity becomes apparent in systems of this
kind, which describes the flow of a two-phase barotropic Korteweg fluid with
capillarity, and allows multiple eigensolutions thus leading to wave-mechanical
effects. We study spontaneous symmetry breaking in the erupting lava which
flows up the conduit, so that fluid fragmentation and nucleation of density
inhomogeneities occur; therefore, changing temperature can trigger a transition
between the "magma-dissolved gas" fluid and magmatic foam phases. This phase
structure is studied by both analytical and numerical methods. In the fluid
phase, cell-like inhomogeneities occur which are described by solitary wave
solutions with a Gaussian density profile; we derive the many-body interaction
potential for these inhomogeneities. For the foam phase, we demonstrate
existence of topological kink solitons which describe bubble-type
inhomogeneities; their stability is ensured by the conservation of a
topological charge.
