Duke Mathematical Journal

Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics. Advance publication of articles online is available.

Conserved energies for the cubic nonlinear Schrödinger equation in one dimensionVolume 167, Number 17 (2018)
Compactification of strata of Abelian differentialsVolume 167, Number 12 (2018)
Generalized Heegner cycles and $p$ -adic Rankin $L$ -seriesVolume 162, Number 6 (2013)
The central limit theorem for dependent random variablesVolume 15, Number 3 (1948)
Independence of $\ell$ for the supports in the decomposition theoremVolume 167, Number 10 (2018)
• ISSN: 0012-7094 (print), 1547-7398 (electronic)
• Publisher: Duke University Press
• Discipline(s): Mathematics
• Full text available in Euclid: 1935--
• Access: By subscription only
• Euclid URL: https://projecteuclid.org/dmj

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MR Citation Database MCQ (2017): 2.45
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Eigenfactor: Duke Mathematical Journal
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Featured article

Conserved energies for the cubic nonlinear Schrödinger equation in one dimension

Volume 167, Number 17 (2018)
Abstract

We consider the cubic nonlinear Schrödinger (NLS) equation as well as the modified Korteweg–de Vries (mKdV) equation in one space dimension. We prove that for each $s\gt -\frac{1}{2}$ there exists a conserved energy which is equivalent to the $H^{s}$-norm of the solution. For the Korteweg–de Vries (KdV) equation, there is a similar conserved energy for every $s\ge -1$.