Integrable Lagrangians and modular forms

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dc.creatorFerapontov, E. V.
dc.creatorOdesskii, A. V.
dc.date2007-07-23
dc.date2007-11-28
dc.date.accessioned2026-07-07T08:45:11Z
dc.date.available2026-07-07T08:45:11Z
dc.descriptionWe investigate non-degenerate Lagrangians of the form $$ \int f(u_x, u_y, u_t) dx dy dt $$ such that the corresponding Euler-Lagrange equations $ (f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0 $ are integrable by the method of hydrodynamic reductions. We demonstrate that the integrability conditions, which constitute an involutive over-determined system of fourth order PDEs for the Lagrangian density f, are invariant under a 20-parameter group of Lie-point symmetries whose action on the moduli space of integrable Lagrangians has an open orbit. The density of the `master-Lagrangian' corresponding to this orbit is shown to be a modular form in three variables defined on a complex hyperbolic ball. We demonstrate how the knowledge of the symmetry group allows one to linearise the integrability conditions.
dc.description17 pages, latex
dc.identifierhttps://arxiv.org/abs/0707.3433
dc.identifierhttp://arxiv.org/abs/0707.3433
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142895
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectDifferential Geometry
dc.subjectNumber Theory
dc.titleIntegrable Lagrangians and modular forms
dc.typetext

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