Hasimoto frames and the Gibbs measure of the periodic nonlinear Schrödinger equation

DOI10.1063/5.0169792arXiv2205.12868OpenAlexW4391735013MaRDI QIDQ6122997

Azadeh Khaleghi, Unnamed Author, Gordon Blower

Publication date: 4 March 2024

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.12868

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs with measure (35R06)

Cites Work

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• Derivation of nonlinear Gibbs measures from many-body quantum mechanics
• Quantitative concentration inequalities for empirical measures on non-compact spaces
• A note on the NLS and the Schrödinger flow of maps
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Periodic nonlinear Schrödinger equation and invariant measures
• Renormalized differential geometry on path space: Structural equation, curvature
• Statistical mechanics of nonlinear wave equations. IV: Cubic Schrödinger
• Logarithmic Sobolev inequalities for pinned loop groups
• Statistical mechanics of the nonlinear Schrödinger equation.
• Classical field theory limit of many-body quantum Gibbs states in 2D and 3D
• Adaptive test of independence based on HSIC measures
• Prékopa-Leindler type inequalities on Riemannian manifolds, Jacobi fields, and optimal transport
• On the geometry of metric measure spaces. II
• Permutations, matrices, and generalized Young tableaux
• Rigorous derivation of the cubic NLS in dimension one
• Transformations of Wiener integrals under translations
• Logarithmic Sobolev inequalities and spectral concentration for the cubic Schrödinger equation
• A logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg–de Vries equation
• Noncommutative Poisson Algebras
• [https://portal.mardi4nfdi.de/wiki/Publication:4342735 Action-angle variables for the cubic Schr�dinger equation]
• Numerical Methods for Stochastic Differential Equations in Matrix Lie Groups Made Simple
• Concentration of measure on product spaces with applications to Markov processes
• A soliton on a vortex filament
• Optimal Transport
• Concentration of the invariant measures for the periodic Zakharov, KdV, NLS and Gross-Piatevskii equations in \(1D\) and \(2D\)