Hasimoto frames and the Gibbs measure of periodic nonlinear Schrödinger Equation
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909324463308800 |
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| author | Blower, Gordon Khaleghi, Azadeh Kuchemann-Scales, Moe |
| author_facet | Blower, Gordon Khaleghi, Azadeh Kuchemann-Scales, Moe |
| contents | The paper interprets the cubic nonlinear Schrödinger equation as a Hamiltonian system with infinite dimensional phase space. There is a Gibbs measure which is invariant under the flow associated with the canonical equations of motion. The logarithmic Sobolev and concentration of measure inequalities hold for the Gibbs measures, and here are extended to the $k$-point correlation function and distributions of related empirical measures. By Hasimoto's theorem, NLSE gives a Lax pair of coupled ODE for which the solutions give a system of moving frames. The paper studies the evolution of the measure induced on the moving frames by the Gibbs measure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_12868 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hasimoto frames and the Gibbs measure of periodic nonlinear Schrödinger Equation Blower, Gordon Khaleghi, Azadeh Kuchemann-Scales, Moe Analysis of PDEs Probability 35Q82, 37L55, 35Q55 The paper interprets the cubic nonlinear Schrödinger equation as a Hamiltonian system with infinite dimensional phase space. There is a Gibbs measure which is invariant under the flow associated with the canonical equations of motion. The logarithmic Sobolev and concentration of measure inequalities hold for the Gibbs measures, and here are extended to the $k$-point correlation function and distributions of related empirical measures. By Hasimoto's theorem, NLSE gives a Lax pair of coupled ODE for which the solutions give a system of moving frames. The paper studies the evolution of the measure induced on the moving frames by the Gibbs measure. |
| title | Hasimoto frames and the Gibbs measure of periodic nonlinear Schrödinger Equation |
| topic | Analysis of PDEs Probability 35Q82, 37L55, 35Q55 |
| url | https://arxiv.org/abs/2205.12868 |