We prove that the nonlinear part H∗ of the KdV Hamiltonian Hkdv, when expressed in action variables I=(In)n≥1, extends to a real analytic function on the positive quadrant ℓ2+(N) of ℓ2(N) and is strictly concave near 0. As a consequence, the differential of H∗ defines a local diffeomorphism near 0 of ℓ2C(N).
On the Convexity of the KdV Hamiltonian / Kappeler, T.; Maspero, A.; Molnar, J.; Topalov, P.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 346:1(2016), pp. 191-236. [10.1007/s00220-015-2563-x]
On the Convexity of the KdV Hamiltonian
Maspero, A.;
2016-01-01
Abstract
We prove that the nonlinear part H∗ of the KdV Hamiltonian Hkdv, when expressed in action variables I=(In)n≥1, extends to a real analytic function on the positive quadrant ℓ2+(N) of ℓ2(N) and is strictly concave near 0. As a consequence, the differential of H∗ defines a local diffeomorphism near 0 of ℓ2C(N).File in questo prodotto:
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