Lyapunov stability of ground states of nonlinear dispersive evolution equations

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Publication:3724772

DOI10.1002/cpa.3160390103zbMath0594.35005OpenAlexW1966652217MaRDI QIDQ3724772

Michael I. Weinstein

Publication date: 1986

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160390103




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Cites Work