Abstract We consider the discrete defocusing nonlinear Schrödinger equation in its integrable version, which is called defocusing Ablowitz–Ladik lattice. We consider periodic boundary conditions with period N and initial data sampled according to the Generalized Gibbs ensemble. In this setting, the Lax matrix of the Ablowitz–Ladik lattice is a random CMV-periodic matrix and it is related to the Killip-Nenciu Circular $$\beta $$ β -ensemble at high-temperature. We obtain the generalized free energy of the Ablowitz–Ladik lattice and the density of states of the random Lax matrix by establishing a mapping to the one-dimensional log-gas. For the Gibbs measure related to the Hamiltonian of the Ablowitz–Ladik flow, we obtain the density of states via a particular solution of the double-confluent Heun equation.
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Performance assessment of the maximum likelihood ensemble filter and the ensemble Kalman filters for nonlinear problems
- Award ID(s):
- 1723191
- NSF-PAR ID:
- 10421236
- Date Published:
- Journal Name:
- Research in the Mathematical Sciences
- Volume:
- 9
- Issue:
- 4
- ISSN:
- 2522-0144
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation