Work

On nonlinear profile decompositions and scattering for a NLS-ODE model

Year: 2017

Type: preprint

Abstract: In this paper, we consider a Hamiltonian system combining a nonlinear Schr\" odinger equation (NLS) and an ordinary differential equation (ODE). This system is a simplified model of the NLS around soliton solutions. Following Nakanishi \cite{NakanishiJMSJ}, we show scattering of $L^2$ small $H^1$ radial solutions. The proof is based on Nakanishi's framework and Fermi Golden Rule estimates on $L^4$ in time norms.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1701.02849

Authors: Cuccagna, Scipio, Maeda, Masaya

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: Analysis of large time behavior of solution to nonlinear partial differential equations with dispersion, Analysis of concentration phenomena for nonlinear wave and dispersive equations, Study of long time behavior of nonlinear dispersive equations via Hamiltonian structure

OpenAlex ID: W2571610035

Cites: 15

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Related to: 10