Communications in Mathematical Physics

, Volume 255, Issue 3, pp 629–653

Ground State of N Coupled Nonlinear Schrödinger Equations in Rn,n≤3


DOI: 10.1007/s00220-005-1313-x

Cite this article as:
Lin, TC. & Wei, J. Commun. Math. Phys. (2005) 255: 629. doi:10.1007/s00220-005-1313-x


We establish some general theorems for the existence and nonexistence of ground state solutions of steady-state N coupled nonlinear Schrödinger equations. The sign of coupling constants βij’s is crucial for the existence of ground state solutions. When all βij’s are positive and the matrix Σ is positively definite, there exists a ground state solution which is radially symmetric. However, if all βij’s are negative, or one of βij’s is negative and the matrix Σ is positively definite, there is no ground state solution. Furthermore, we find a bound state solution which is non-radially symmetric when N=3.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsNational Taiwan UniversityTaipeiTaiwan, R.O.C
  2. 2.Department of MathematicsThe Chinese University of Hong KongShatinHong Kong, P.R. China

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