Solutions with compact time spectrum to nonlinear Klein--Gordon and Schroedinger equations and the Titchmarsh theorem for partial convolution
Analysis of PDEs
2021-01-01 v4 Mathematical Physics
Functional Analysis
math.MP
Pattern Formation and Solitons
Abstract
We prove that finite energy solutions to the nonlinear Schroedinger equation and nonlinear Klein--Gordon equation which have the compact time spectrum have to be one-frequency solitary waves. The argument is based on the generalization of the Titchmarsh convolution theorem to partial convolutions.
Keywords
Cite
@article{arxiv.1810.09047,
title = {Solutions with compact time spectrum to nonlinear Klein--Gordon and Schroedinger equations and the Titchmarsh theorem for partial convolution},
author = {Andrew Comech},
journal= {arXiv preprint arXiv:1810.09047},
year = {2021}
}
Comments
15 pages