Stability of ground-states for a system of M coupled semilinear Schrödinger equations

Abstract

We focus on the study of the stability properties of ground-states for the system of M coupled semilinear Schrödinger equations with power-type nonlinearities and couplings. Our results are generalizations of the theory for the single equation and the technique used is a simplification of the original one. Depending on the power of the nonlinearity, we may observe stability, instability and weak instability. We also obtain results for three distinct classes of bound-states, which is a special feature of the \({M \geqslant 2}\) case.

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Correspondence to Simão Correia.

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Correia, S. Stability of ground-states for a system of M coupled semilinear Schrödinger equations. Nonlinear Differ. Equ. Appl. 23, 26 (2016). https://doi.org/10.1007/s00030-016-0379-9

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Mathematics Subject Classification

  • 35Q55
  • 35B35
  • 35B40

Keywords

  • Coupled semilinear Schrödinger equations
  • Ground-states
  • Stability