Work

Lepage equivalents for second–order Lagrangians and applications: 2D modified higher–order Boussinesq–type equations

Year: 2025

Type: article

Abstract: In the frame of the Lagrangian formalism on [Formula: see text]-order prolongations of fibered manifolds and related structures such as (prolongation of) projectable vector fields, (sheaves of) differential forms and contact structures, we propose a Lagrangian two-field derivation of [Formula: see text] modified Boussinesq equation, obtained as coupled systems of Euler–Lagrange (E–L) equations for the two fields. By means of a recursive formula involving geometric integration by parts formulae, we construct extended ‘full’ equivalents of such Lagrangians, in particular of Krupka–Betounes type, by which the equations are obtained straightly as the [Formula: see text]-contact component of their exterior differential. As a main result, we find new [Formula: see text] fourth- and sixth-order modified Boussinesq-type equations, containing mixed terms in both the spatial variables [Formula: see text] and [Formula: see text]. As a byproduct, we also obtain a [Formula: see text]-field variational characterization of the stationary reduction of the moving-frame (according to Bogdanov and Zakharov) KP equation.

Source: International Journal of Geometric Methods in Modern Physics

DOI: 10.1142/s0219887826500350

Authors: Marcella Palese, Fabrizio Zanello

Institutions: University of Turin, University of Potsdam

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Università degli Studi di Torino

Awards: G3490009754, G7630636939