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)
Cohomologically induced distinguished representations and cohomological test vectorsVolume 168, Number 1 (2019)
Mirror symmetry for the Landau–Ginzburg $A$ -model $M=\mathbb{C}^{n}$ , $W=z_{1}\cdots z_{n}$Volume 168, Number 1 (2019)
Legendrian fronts for affine varietiesAdvance publication (2019)
Simplicity of the $C\sp{\ast}$ -algebra associated with the free group on two generatorsVolume 42, Number 1 (1975)
• 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

In Memoriam

The Duke Mathematical Journal notes with sadness the passing of the distinguished mathematician Jean Bourgain, a current Editor of DMJ who served the journal faithfully for 28 years.

Richard Hain and Jonathan Wahl
Managing Editors

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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 $s\ge -1$.

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