Lagrangian multiforms and dispersionless integrable systems
arXiv:2503.22615 · doi:10.1007/s11005-025-02016-w
Abstract
We demonstrate that interesting examples of Lagrangian multiforms appear naturally in the theory of multidimensional dispersionless integrable systems as (a) higher-order conservation laws of linearly degenerate PDEs in 3D, and (b) in the context of Gibbons-Tsarev equations governing hydrodynamic reductions of heavenly type equations in 4D.
25 pages. v2: extended introduction and other minor improvements and corrections