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Blow-up solutions to nonlinear Schrödinger system at multiple points

  • Yiming Su
  • Qing GuoEmail author
Article
  • 55 Downloads

Abstract

In this paper, we consider finite-time blow-up solutions to the following N coupled nonlinear Schrödinger system in \(\mathbb {R}^2\):
$$\begin{aligned}i\partial _t\phi _j+\Delta \phi _j+\sum _{k=1}^{N}a_{jk}|\phi _k|^2\phi _j=0, \quad j=1,2,\ldots ,N,\quad (0.1) \end{aligned}$$
where \(N\ge 2\) and the coefficient matrix A satisfies \(a_{jk}=a_{kj}\) and \(a_{jj}>0\) for \(1\le j,k\le N\). We construct finite-time blow-up solutions concentrating at arbitrary K different points with \(K\ge N\).

Keywords

Schrödinger system Blow-up solution Multiple-point concentration 

Mathematics Subject Classification

35Q55 37K40 

Notes

Acknowledgments

The authors would like to express their gratitude to the referees for useful comments. This work was supported by the National Natural Science Foundation of China (Nos. 11601482, 11301564, 11771469) and the Zhejiang Provincial NSFC (No. LQ15A010006).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.College of ScienceZhejiang University of TechnologyHangzhouPeople’s Republic of China
  2. 2.College of ScienceMinzu University of ChinaBeijingPeople’s Republic of China

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