Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 417, Issue 1, Pages 180-199Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2014.02.063
Keywords
Soliton dynamics; Choquard equation; Hartree equation; Modulational stability; Ground states
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Funding
- MIUR project: Variational and Topological Methods in the Study of Nonlinear Phenomena
- Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of Istituto Nazionale di Alta Matematica (INdAM)
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We investigate the soliton dynamics for a class of nonlinear Schrodinger equations with a non-local nonlinear term. In particular, we consider what we call generalized Choquard equation where the nonlinear term is (vertical bar x vertical bar(theta-N) * vertical bar u vertical bar(p))vertical bar u vertical bar(p-2)u. This problem is particularly interesting because the ground state solutions are not known to be unique or non-degenerate. (C) 2014 Elsevier Inc. All rights reserved.
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