Soliton dynamics for the generalized Choquard equation
Copyright policy )Soliton dynamics for the generalized Choquard equation
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 $(|x|^{θ-N} * |u|^p)|u|^{p-2}u$. This problem is particularly interesting because the ground state solutions are not known to be unique or non-degenerate.
16 pages
- University of Pisa Italy
- Catholic University of the Sacred Heart Italy
- Instituto Politécnico Nacional Mexico
- University of Verona Italy
- Polytechnic University of Bari Italy
NLS equations (nonlinear Schrödinger equations), Soliton dynamics; nonlocal NLS, 35Q51, 35Q40, 35Q41, Soliton dynamics, Choquard equation, Hartree equation, Modulational stability, Ground states, ground states, modulational stability, Integro-partial differential equations, Mathematics - Analysis of PDEs, Soliton solutions, Hartree equation, FOS: Mathematics, Soliton dynamic, Stability in context of PDEs, Analysis of PDEs (math.AP)
NLS equations (nonlinear Schrödinger equations), Soliton dynamics; nonlocal NLS, 35Q51, 35Q40, 35Q41, Soliton dynamics, Choquard equation, Hartree equation, Modulational stability, Ground states, ground states, modulational stability, Integro-partial differential equations, Mathematics - Analysis of PDEs, Soliton solutions, Hartree equation, FOS: Mathematics, Soliton dynamic, Stability in context of PDEs, Analysis of PDEs (math.AP)
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