MathDB5 problems
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Infinite Lenard–Magri extension for the multicomponent Volterra-type equation
Multicomponent Lenard–Magri conjecture. The Lenard–Magri sequence defined by the displayed relations can be infinitely extended; consequently, the resulting differential-difference…
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The infinite Lenard–Magri scheme conjecture for bi-Adler type operators
Infinite Lenard–Magri scheme conjecture. The Lenard–Magri scheme is infinite for each Casimir functional .
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Dubrovin–Zhang conjecture on uniqueness of perturbed bi-Hamiltonian hierarchies
A bi-Hamiltonian hierarchy has a dispersionless limit, obtained by setting the deformation parameter to zero, and its perturbations are considered under suitable additional assumpt…
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Conjecture on non-diagonalizable singular non-locally bi-Hamiltonian systems
Consider non-locally bi-Hamiltonian systems of hydrodynamic type whose pair of metrics is singular, so the non-singularity condition fails. Existence conjecture. There exist non-di…
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Conjecture on non-strictly hyperbolic non-locally bi-Hamiltonian systems
A non-singular (semisimple) non-locally bi-Hamiltonian system of hydrodynamic type has a diagonal matrix of velocities … Such systems are strictly hyperbolic when their eigenvalues…