On discrete rarefaction waves in a nonlinear Schr\"odinger equation toy model for weak turbulence
Classical Analysis and ODEs
2018-04-13 v4 Analysis of PDEs
Abstract
We explore further the rarefaction wave-like solutions recently discussed in work of the second author with J. Colliander, T. Oh and G. Simpson for a model Hamiltonian dynamical system derived by Colliander-Keel-Staffilani-Takaoka-Tao to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus.
Keywords
Cite
@article{arxiv.1307.1873,
title = {On discrete rarefaction waves in a nonlinear Schr\"odinger equation toy model for weak turbulence},
author = {Sebastian Herr and Jeremy L. Marzuola},
journal= {arXiv preprint arXiv:1307.1873},
year = {2018}
}
Comments
24 pages, 5 figures. Contains a brief summary of results from the second author's work with J. Colliander, T. Oh and G. Simpson in arXiv:1209.0827. Improved exposition, fixed typos and added a Numerical Section relating to a connection to the Toda Lattice