2 problems

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Dubrovin–Liu–Zhang's existence conjecture for central invariants
Dubrovin–Liu–Zhang's existence conjecture. For any choice of central-invariant functions $c_i(u^i)$ , the corresponding Miura-equivalence class of deformations is non-empty; equival…
Conjecturesolvedcentral-invariants integrable-systems poisson-geometryarXiv posted 3 days ago
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Existence conjecture for deformations with prescribed central invariants
Let a semisimple bihamiltonian structure of hydrodynamic type and a set of central invariants be given. Existence conjecture. There exists a deformation of the bihamiltonian struct…
Conjecturesolvedbihamiltonian-structures central-invariants integrable-systemsarXiv posted 3 days ago

Dubrovin–Liu–Zhang's existence conjecture for central invariants