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- W2523841213 startingPage "2205" @default.
- W2523841213 abstract "We consider spike vector solutions for the nonlinearSchrödinger systembegin{equation*}left{begin{array}{ll}-varepsilon^{2}Delta u+P(x)u=mu u^{3}+beta v^2u hbox{in} mathbb{R}^3,-varepsilon^{2}Delta v+Q(x)v=nu v^{3} +beta u^2v hbox{in} mathbb{R}^3,u, v >0 , hbox{in} mathbb{R}^3,end{array}right.end{equation*}where $varepsilon > 0$ is a small parameter, $P(x)$ and $Q(x)$ arepositive potentials, $mu>0, nu>0$ are positive constants and$betaneq 0$ is a coupling constant. We investigate the effect ofpotentials and the nonlinear coupling on the solution structure. Forany positive integer $kge 2$, we construct $k$interacting spikes concentrating near the local maximum point$x_{0}$ of $P(x)$ and $Q(x)$ when $P(x_{0})=Q(x_{0})$ in theattractive case. In contrast, for any two positive integers $kge 2$ and $mge 2$, we construct $k$ interacting spikes for $u$near the local maximum point $x_{0}$ of $P(x)$ and $m$ interacting spikes for $v$near the local maximum point $bar{x}_{0}$ of$Q(x)$ respectively when $x_{0}neq bar{x}_{0}$, moreover,spikes of $u$ and $v$ repel each other. Meanwhile, we prove theattractive phenomenon for $beta 0$." @default.
- W2523841213 created "2016-10-07" @default.
- W2523841213 creator A5037678294 @default.
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- W2523841213 date "2015-09-01" @default.
- W2523841213 modified "2023-10-16" @default.
- W2523841213 title "Spike vector solutions for some coupled nonlinear Schrödinger equations" @default.
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- W2523841213 doi "https://doi.org/10.3934/dcds.2016.36.2205" @default.
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