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DOI: 10.5445/IR/1000087314
Veröffentlicht am 08.11.2018

Bifurcations of nontrivial solutions of a cubic Helmholtz system

Mandel, Rainer; Scheider, Dominic

Abstract:
This paper presents local and global bifurcation results for radially symmetric solutions of the cubic Helmholtz system
$\begin{equation*}
\begin{cases} -Δu - μu = \left( u^2 + b \: v^2 \right) u &\text{ on }
\mathbb{R}^3, \\ -Δv - νv = \left( v^2 + b \: u^2 \right) v &\text{ on
} \mathbb{R}^3. \end{cases} \end{equation*}$
It is shown that every point along any given branch of radial semitrivial solutions $(u_0, 0, b)$ or diagonal solutions $(ub,ub,b)$ (for $μ=ν)$ is a bifurcation point. Our analysis is based on a detailed investigation of the oscillatory behavior of solutions at infinity that are shown to decay like $\frac{1}{|x|}$ as $|x|\to\infty$.


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
URN: urn:nbn:de:swb:90-873141
KITopen ID: 1000087314
Verlag KIT, Karlsruhe
Umfang 31 S.
Serie CRC 1173 ; 2018/32
Schlagworte nonlinear Helmholtz sytem, bifurcation
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