Multiple normalized standing-waves solutions to the scalar non-linear Klein-Gordon equation with two competing powers
Analysis of PDEs
2019-10-15 v1
Abstract
In this work we prove the existence of standing-wave solutions to the scalar non-linear Klein-Gordon equation in dimension one and the stability of the ground-state, the set which contains all the minima of the energy constrained to the manifold of the states sharing a fixed charge. For non-linearities which are combinations of two competing powers we prove that standing-waves in the ground-state are orbitally stable. We also show the existence of a degenerate minimum and the existence of two positive and radially symmetric minima having the same charge.
Cite
@article{arxiv.1910.05940,
title = {Multiple normalized standing-waves solutions to the scalar non-linear Klein-Gordon equation with two competing powers},
author = {Daniele Garrisi},
journal= {arXiv preprint arXiv:1910.05940},
year = {2019}
}
Comments
26 pages, 1 figure