Continuum Calogero-Moser models are realized as Hamiltonian systems on L²₊ with mutually commuting conserved quantities, giving a new global well-posedness proof linked to symplectic nondegeneracy and the isoperimetric problem.
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The thermal Toda lattice is modeled as quasiparticles whose locations satisfy an asymptotic scattering relation derived from eigenvector properties of the Lax matrix.
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The Hamiltonian formulation of continuum Calogero-Moser models
Continuum Calogero-Moser models are realized as Hamiltonian systems on L²₊ with mutually commuting conserved quantities, giving a new global well-posedness proof linked to symplectic nondegeneracy and the isoperimetric problem.
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Asymptotic Scattering Relation for the Toda Lattice
The thermal Toda lattice is modeled as quasiparticles whose locations satisfy an asymptotic scattering relation derived from eigenvector properties of the Lax matrix.