Characterization of ground-states for a system of M coupled semilinear Schrödinger equations and applications

2014/10/29 by Correia, Simão
#35B40 #35E15 #35J47 #35Q55 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1410.7993

Abstract

We focus on the study of ground-states for the system of M coupled semilinear Schrödinger equations with power-type nonlinearities and couplings. General results regarding existence and characterization are derived using a variational approach. We show the usefulness of such a characterization in several particular cases, including those for which uniqueness of ground-states is already known. Finally, we apply the results to find the optimal constant for the vector-valued Gagliardo-Nirenberg inequality and we study global existence, L²-concentration phenomena and blowup profile for the evolution system in the L²-critical power case.

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