Unconditional local and global well-posedness proved for the two-parameter MMT equation on the torus in Sobolev spaces, with flow map shown not C^3 at origin for positive derivative order.
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Toda lattice solutions converge globally in time to KdV solutions in the long-wave continuum limit.
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Unconditional Well-posedness for the MMT Equation on the Torus
Unconditional local and global well-posedness proved for the two-parameter MMT equation on the torus in Sobolev spaces, with flow map shown not C^3 at origin for positive derivative order.
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The Korteweg-de Vries limit for the global dynamics of the Toda lattice
Toda lattice solutions converge globally in time to KdV solutions in the long-wave continuum limit.