Effective Dynamics of the Vector Nonlinear Schr\"odinger Equations on Large Domains
Analysis of PDEs
2022-01-05 v1 Classical Analysis and ODEs
Abstract
We consider the vector nonlinear Schr\"odinger equation posed on the box with periodic boundary conditions, and derive the continuous resonant (CR) equation that describes the effective dynamics for large box size and small data size over very large time-scales. Moreover, we investigate various properties of the continuous resonant equations, including the Hamiltonian structure and the well-posedness, etc..
Keywords
Cite
@article{arxiv.2201.00861,
title = {Effective Dynamics of the Vector Nonlinear Schr\"odinger Equations on Large Domains},
author = {Katherine Zhiyuan Zhang},
journal= {arXiv preprint arXiv:2201.00861},
year = {2022}
}