Soliton dynamics for the generalized Choquard equation

2013/10/11 by Bonanno, Claudio, d'Avenia, Pietro, Ghimenti, Marco +1 · 2 citations
#35Q40 #35Q41 #35Q51 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.3067

Abstract

We investigate the soliton dynamics for a class of nonlinear Schrödinger equations with a non-local nonlinear term. In particular, we consider what we call \em generalized Choquard equation where the nonlinear term is (|x|^θ-N * |u|^p)|u|^p-2u. This problem is particularly interesting because the ground state solutions are not known to be unique or non-degenerate.

Cited by

• Ground states for the Hartree energy functional in the critical case
• Uniqueness and stability of normalized ground states for Hartree equation with a harmonic potential

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