Ground state solutions for a coupled nonlinear Schrödinger-KdV system
首发时间:2020-02-21
Abstract:In this paper, we study the following Schr\"{o}dinger-KdV system \begin{align*} \begin{cases} -\triangle u+\lambda_{1}u=u^{3}-\beta uv, &u\in H^{1}(\mathbb {R}^N),\\ -\triangle v+\lambda_{2}v=\frac{1}{2}|v|v-\frac{\beta}{2}u^{2}, &v\in H^1(\mathbb{R}^N), \end{cases} \end{align*}where λi is a constant, $i=1,2$ and $N=1,2,3$. We obtain the existence of ground state solutions for the above system by using the variational methods,the Nehari manifold and and some analysis techniques.
keywords: Partial differential equation Schrödinger-KdV system Variational methods Ground state solutions
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一类耦合非线性Schrödinger-KdV系统基态解的存在性
摘要:在这篇文章中,我们研究了一类耦合非线性Schrödinger-KdV系统\begin{align*} \begin{cases} -\triangle u+\lambda_{1}u=u^{3}-\beta uv, &u\in H^{1}(\mathbb {R}^N),\\ -\triangle v+\lambda_{2}v=\frac{1}{2}|v|v-\frac{\beta}{2}u^{2}, &v\in H^1(\mathbb{R}^N), \end{cases} \end{align*}其中λi是一个常数,$i=1,2$,当$N=1,2,3$时,利用变分方法, Nehari-流形和各种分析技巧, 对耦合参数的范围进行讨论, 得到了该系统非平凡基态解的存在性结果。
关键词: 偏微分方程 Schrödinger-KdV系统 变分法 基态解
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一类耦合非线性Schrödinger-KdV系统基态解的存在性
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