Multiple normalized standing-waves solutions to the scalar non-linear Klein-Gordon equation with two competing powers

Daniele Garrisi

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arXiv · 1910.05940

Multiple normalized standing-waves solutions to the scalar non-linear Klein-Gordon equation with two competing powers

Daniele Garrisi

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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.

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Daniele Garrisi. 2019-10-14. Multiple normalized standing-waves solutions to the scalar non-linear Klein-Gordon equation with two competing powers. https://arxiv.org/abs/1910.05940

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