Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations

Original Article

DOI: 10.1007/s00526-006-0079-0

Cite this article as:
Ambrosetti, A., Colorado, E. & Ruiz, D. Calc. Var. (2007) 30: 85. doi:10.1007/s00526-006-0079-0


This paper is devoted to study a class of systems of nonlinear Schrödinger equations: \(\left\{\begin{array}{rcl} -\Delta u+u-u^{3}=\epsilon v, \\ -\Delta v+v-v^{3}=\epsilon u, \end{array}\right.\) in \(\mathbb{R}^{n}\) with dimension n = 1,2,3. Our main result states that if \(\mathcal{P}\) denotes a regular polytope centered at the origin of \(\mathbb{R}^{n}\) such that its side is greater than the radius, then there exists a solution with one multi-bump component having bumps located near the vertices of \(\xi\mathcal{P}\), where \({\xi\sim \log(1/\varepsilon)}\), while the other component has one negative peak.

Mathematics Subject Classification (2000)

36J60 35J20 35Q55 

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.SISSATriesteItaly
  2. 2.Dep. Análisis MatemáticoUniv. GranadaGranadaSpain

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