Spectra of positive and negative energies in the linearized NLS problem
Communications on Pure and Applied Mathematics, ISSN: 0010-3640, Vol: 58, Issue: 1, Page: 1-29
2005
- 94Citations
- 10Captures
Metric Options: Counts1 Year3 YearSelecting the 1-year or 3-year option will change the metrics count to percentiles, illustrating how an article or review compares to other articles or reviews within the selected time period in the same journal. Selecting the 1-year option compares the metrics against other articles/reviews that were also published in the same calendar year. Selecting the 3-year option compares the metrics against other articles/reviews that were also published in the same calendar year plus the two years prior.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Article Description
We study the spectrum of the linearized NLS equation in three dimensions in association with the energy spectrum. We prove that unstable eigenvalues of the linearized NLS problem are related to negative eigenvalues of the energy spectrum, while neutrally stable eigenvalues may have both positive and negative energies. The nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum. We derive bounds on the number of unstable eigenvalues of the linearized NLS problem and study bifurcations of embedded eigenvalues of positive and negative energies. We develop the L -scattering theory for the linearized NLS operators and recover results of Grillakis [5] with a Fermi golden rule. © 2004 Wiley Periodicals, Inc.
Bibliographic Details
Provide Feedback
Have ideas for a new metric? Would you like to see something else here?Let us know