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Ten new insights in climate science 2020 – a horizon scan
- Erik Pihl, Eva Alfredsson, Magnus Bengtsson, Kathryn J. Bowen, Vanesa Cástan Broto, Kuei Tien Chou, Helen Cleugh, Kristie Ebi, Clea M. Edwards, Eleanor Fisher, Pierre Friedlingstein, Alex Godoy-Faúndez, Mukesh Gupta, Alexandra R. Harrington, Katie Hayes, Bronwyn M. Hayward, Sophie R. Hebden, Thomas Hickmann, Gustaf Hugelius, Tatiana Ilyina, Robert B. Jackson, Trevor F. Keenan, Ria A. Lambino, Sebastian Leuzinger, Mikael Malmaeus, Robert I. McDonald, Celia McMichael, Clark A. Miller, Matteo Muratori, Nidhi Nagabhatla, Harini Nagendra, Cristian Passarello, Josep Penuelas, Julia Pongratz, Johan Rockström, Patricia Romero-Lankao, Joyashree Roy, Adam A. Scaife, Peter Schlosser, Edward Schuur, Michelle Scobie, Steven C. Sherwood, Giles B. Sioen, Jakob Skovgaard, Edgardo A. Sobenes Obregon, Sebastian Sonntag, Joachim H. Spangenberg, Otto Spijkers, Leena Srivastava, Detlef B. Stammer, Pedro H. C. Torres, Merritt R. Turetsky, Anna M. Ukkola, Detlef P. van Vuuren, Christina Voigt, Chadia Wannous, Mark D. Zelinka
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- Journal:
- Global Sustainability / Volume 4 / 2021
- Published online by Cambridge University Press:
- 27 January 2021, e5
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- Article
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- Open access
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Non-technical summary
We summarize some of the past year's most important findings within climate change-related research. New research has improved our understanding of Earth's sensitivity to carbon dioxide, finds that permafrost thaw could release more carbon emissions than expected and that the uptake of carbon in tropical ecosystems is weakening. Adverse impacts on human society include increasing water shortages and impacts on mental health. Options for solutions emerge from rethinking economic models, rights-based litigation, strengthened governance systems and a new social contract. The disruption caused by COVID-19 could be seized as an opportunity for positive change, directing economic stimulus towards sustainable investments.
Technical summaryA synthesis is made of ten fields within climate science where there have been significant advances since mid-2019, through an expert elicitation process with broad disciplinary scope. Findings include: (1) a better understanding of equilibrium climate sensitivity; (2) abrupt thaw as an accelerator of carbon release from permafrost; (3) changes to global and regional land carbon sinks; (4) impacts of climate change on water crises, including equity perspectives; (5) adverse effects on mental health from climate change; (6) immediate effects on climate of the COVID-19 pandemic and requirements for recovery packages to deliver on the Paris Agreement; (7) suggested long-term changes to governance and a social contract to address climate change, learning from the current pandemic, (8) updated positive cost–benefit ratio and new perspectives on the potential for green growth in the short- and long-term perspective; (9) urban electrification as a strategy to move towards low-carbon energy systems and (10) rights-based litigation as an increasingly important method to address climate change, with recent clarifications on the legal standing and representation of future generations.
Social media summaryStronger permafrost thaw, COVID-19 effects and growing mental health impacts among highlights of latest climate science.
15 - Inverse Scattering for the Matrix Schrö Equation with Non-Hermitian Potential
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- By Peter Schuur
- Edited by Lokenath Debnath
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- Book:
- Nonlinear Waves
- Published online:
- 29 October 2009
- Print publication:
- 30 December 1983, pp 285-297
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Summary
INTRODUCTION.
Kamijo and Wadati (1974) developed an inverse scattering formalism for the matrix Schrödinger equation with Hermitian potential matrix U(x). Assuming a similar formalism in the non-Hermitian case the authors and later on Calogero and Degasperis (1976) found several classes of solvable nonlinear evolution equations. To our knowledge this assumption has nowhere been justified in the literature. Indeed, Wadati (1980) writes: “At the moment, it is an open question as to what are the most general conditions for which the inverse scattering problem can be solved. I have considered three cases:
The first crucial point in the discussions is the definition of the Wronskian. Although we need extra assumptions, similar arguments seem to be valid”.
The present paper is an attempt to settle this question. We consider the Schrödinger scattering problem for any continuous potential matrix U(x) decaying sufficiently rapidly for continuous potential matrix U(x) decaying sufficiently rapidly for. Superimposing some rather natural regularity conditions on the right transmission coefficient that are partly familiar from the Zakharov-Shabat scattering problem (Eckhaus and van Harten, 1981), we show that - apart from the unique solvability of the Gel'fand-Levitan-Marchenko equation - the inverse scattering problem can be solved completely. Though initially the approach parallels that of Kamijo and Wadati (1974), our ways split up in Section 5. The reason is that the Wronskians employed by Kamijo and Wadati to extend the scattering coefficients to the upper half plane are of no use in the non-Hermitian case. To circumvent this difficulty, we perform the extension by means of integral representations in terms of the potential and the Jost functions.
NOTATION.
Throughout, we shall use the following notation:
The determinant of A will be denoted by det A. I is the n x n identity matrix. We set
Our notation for the Jost functions, scattering coefficients, etc. closely resembles that used in Eckhaus and van Harten (1981). This notation is different from the one in Kamijo and Wadati (1974). For convenience, we specify here the relation between these different notations: