Well-posedness of higher-order nonlinear Schrödinger equations in Sobolev spaces \(H^{s}(\mathbb R^{n})\) and applications

DOI10.1016/j.na.2006.06.020zbMath1123.35064OpenAlexW1975028093MaRDI QIDQ881603

Cuihua Guo, Shang-bin Cui

Publication date: 30 May 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.06.020

zbMATH Keywords

conservation lawsCauchy problemglobal well-posednessdispersive equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

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• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• On the (generalized) Korteweg-de Vries equation
• Self-Focusing with Fourth-Order Dispersion
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle

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