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The higher-dimensional pluri-Lagrangian form conjecture for integrable PDE hierarchies
Higher-dimensional pluri-Lagrangian form conjecture. For $d>2$ , integrable hierarchies of $d$ -dimensional integrable partial differential equations can be described by pluri-Lagran…
Conjectureopenintegrable-pdes pluri-lagrangian-systems variational-calculusarXiv posted 2 days ago
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Ferapontov's conjecture on multidimensional hydrodynamically integrable PDEs
A second-order PDE of Hirota type is a multidimensional hydrodynamically integrable PDE whose precise general form is not specified in the statement. A PDE is of Monge--Ampère type…
Conjectureopenintegrable-pdes monge-ampere-equations nonlinear-pdesarXiv posted 2 days ago
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Conjecture on integrable dispersionless Hirota equations
Let $u=u(x^1,ots,x^n)$ be a function of $n$ independent variables, and let $u_{ij}$ denote its second-order partial derivatives. A dispersionless Hirota equation is a relation … It…
Conjectureopenintegrable-pdes monge-ampere-equations symplectic-geometryarXiv posted 2 days ago

The higher-dimensional pluri-Lagrangian form conjecture for integrable PDE hierarchies