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Soliton dynamics for the generalized Choquard equation. (English) Zbl 1332.35066

Summary: 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 generalized Choquard equation, where the nonlinear term is \((| x|^{\theta-N}\ast| u|^p)| u|^{p-2}u\). This problem is particularly interesting because the ground state solutions are not known to be unique or non-degenerate.

MSC:

35C08 Soliton solutions
35Q55 NLS equations (nonlinear Schrödinger equations)
35R09 Integro-partial differential equations
35B35 Stability in context of PDEs
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