Breather Solutions of the Cubic Klein-Gordon Equation release_fmasjkjzgnh35mth477vkesmhm

by Dominic Scheider

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(2020)

Abstract

We obtain real-valued, time-periodic and radially symmetric solutions of the cubic Klein-Gordon equation ∂_t^2 U - Δ U + m^2 U = Γ (x) U^3 on R×R^3, which are weakly localized in space. Various families of such "breather" solutions are shown to bifurcate from any given nontrivial stationary solution. The construction of weakly localized breathers in three space dimensions is, to the author's knowledge, a new concept and based on the reformulation of the cubic Klein-Gordon equation as a system of coupled nonlinear Helmholtz equations involving suitable conditions on the far field behavior.
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Type  article
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Date   2020-01-13
Version   v1
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arXiv  2001.04108v1
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