3 problems

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Existence of a second Hamiltonian structure for the reduced partial difference equation
Second Hamiltonian structure conjecture. The equation possesses a second Hamiltonian structure, whose form is more complicated than the one displayed above. The conjecture asserts…
Conjectureopenhamiltonian-systems partial-difference-equations poisson-structuresarXiv posted 2 days ago
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Co-primeness as a criterion for singularity confinement and integrability
A nonlinear partial difference equation is said to have singularity confinement when its singularities do not propagate indefinitely, and two terms are co-prime when they share no…
Conjectureopenintegrable-systems partial-difference-equations singularity-confinementarXiv posted 2 days ago
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The discrete Calogero–Eckhaus conjecture for multiscale reductions
A nonlinear dispersive $\mathbb{Z}^2$ -lattice equation is considered together with its lowest-order multiscale reduction, obtained through the multiscale expansion formalism. The r…
Conjectureopenintegrable-systems multiscale-analysis partial-difference-equationsarXiv posted 2 days ago

Existence of a second Hamiltonian structure for the reduced partial difference equation