Deng, Qingquan; Soffer, Avy; Yao, Xiaohua Soliton-potential interactions for nonlinear Schrödinger equation in \(\mathbb{R}^3\). (English) Zbl 1428.35500 SIAM J. Math. Anal. 50, No. 5, 5243-5292 (2018). Summary: In this work we mainly consider the dynamics and scattering of a narrow soliton of the nonlinear Schrödinger equation with a potential in \(\mathbb{R}^3\), where the asymptotic state of the system can be far from the initial state in parameter space. Specifically, if we let a narrow soliton state with initial velocity \(\upsilon_{0}\) of order \(1\) interact with an external potential \(V(x)\), then the velocity \(\upsilon_{+}\) of outgoing solitary wave in infinite time will in general be very different from \(\upsilon_{0}\). In contrast to our present work, previous results proved that the soliton is asymptotically stable so that \(\upsilon_{+}\) stays close to \(\upsilon_{0}\) for all times. Cited in 4 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 35B40 Asymptotic behavior of solutions to PDEs 35C08 Soliton solutions 35P25 Scattering theory for PDEs Keywords:endpoint Strichartz estimates; soliton-potential interaction; asymptotic stability PDFBibTeX XMLCite \textit{Q. Deng} et al., SIAM J. Math. Anal. 50, No. 5, 5243--5292 (2018; Zbl 1428.35500) Full Text: DOI arXiv References: [1] J. E. Avron, R. Seiler, and L. G. Yaffe, Adiabatic theorems and applications to the quantum hall effect, Comm. Math. Phys., 110 (1987), pp. 33–49. · Zbl 0626.58033 [2] W. K. Abou Salem and C. Sulem, Resonant tunneling of fast solitons through large potential barriers, Canad. J. Math., 63 (2011), pp. 1201–1219. · Zbl 1247.35152 [3] W. K. Abou Salem, Solitary wave dynamics in time-dependent potentials, J. Math. Phys., 49 (2008), 032101. · Zbl 1153.81428 [4] W. K. 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