Solitons and Scattering for the Cubic–Quintic Nonlinear Schrödinger Equation on $${\mathbb{R}^3}$$ R 3
作者： Rowan Killip , Tadahiro Oh , Oana Pocovnicu , Monica Vişan
DOI: 10.1007/S00205-017-1109-0
关键词: Type (model theory) 、 Operator (physics) 、 Partial differential equation 、 Nonlinear Schrödinger equation 、 Mathematics 、 Virial theorem 、 Soliton 、 Quintic function 、 Mathematical analysis 、 Context (language use)
摘要: We consider the cubic–quintic nonlinear Schrodinger equation: $$i\partial_t u = -\Delta - |u|^2u + |u|^4u.$$ In first part of paper, we analyze one-parameter family ground state solitons associated to this equation with particular attention shape mass/energy curve. Additionally, are able characterize kernel linearized operator about such and demonstrate that they occur as optimizers for a inequalities Gagliardo–Nirenberg type. Building on work, in latter paper prove scattering holds solutions belonging region \({{\mathcal{R}}}\) plane where virial is positive. show partially bounded by also rescalings (which not soliton their own right). The discovery rescaled context new highlights an unexpected limitation any virial-based methodology.
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