# Nonlinear wave-mechanical effects in Korteweg fluid magma transport

## TL;DR

This paper explores wave-mechanical effects in magma transport using a nonlinear wave equation, revealing phenomena like symmetry breaking, phase transitions, and solitary wave solutions in volcanic conduits.

## Contribution

It introduces a novel nonlinear wave equation with logarithmic nonlinearity to model magma flow, capturing phase transitions and inhomogeneities in volcanic conduits.

## Key findings

- Identification of wave-mechanical effects in magma transport.
- Existence of solitary wave solutions with Gaussian profiles.
- Demonstration of topological kink solitons in foam phases.

## Abstract

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.