DOI: 10.1209/epl/i2003-00547-6
Europhys. Lett., 63 (3) , pp. 472-475 (2003)

Logarithmic Schrödinger-like equation as a model for magma transport

S. De Martino^{1, 2, 3}, M. Falanga^{1, 2}, C. Godano^{4, 5} and G. Lauro<sup>6

1</sup>  Dipartimento di Fisica, Università di Salerno Via S. Allende, 84081 Baronissi (SA), Italy
²  INFM, Unità di Salerno - 84081 Baronissi (SA), Italy
³  INFN, Gruppo Collegato di Salerno - 84081 Baronissi (SA), Italy
⁴  Dipartimento di Scienze Ambientali, II Università di Napoli - Caserta, Italy
⁵  INFM, UdR di Napoli, Gruppo Coordinato SUN
⁶  Dipartimento di Matematica Applicata, Università di Firenze - Firenze, Italy

demartino@sa.infn.it
rosfal@sa.infn.it
cataldo.godano@unina2.it
lauro@dma.unifi.it

(Received 23 January 2003; accepted in final form 5 June 2003)

Abstract
We show that, under a suitable assumption on the pressure tensor, the mass and momentum balance equations of hydrodynamical theory, introduced in the early 1980s by many authors to describe matrix separation, yield the equations of the Madelung fluid that are equivalent to the Schrödinger-like equation with logarithmic nonlinearity. This equation has solitary-waves solutions as required by many experimental volcanic models.

PACS
91.40.Ft - Eruptions.
47.10.+g - Fluid dynamics: General theory.
05.45.Yv - Solitons.

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