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Advances in Mathematical Physics
Volume 2011 (2011), Article ID 854719, 4 pages
Justification of the NLS Approximation for the KdV Equation Using the Miura Transformation
IADM, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
Received 4 March 2011; Accepted 16 March 2011
Academic Editor: Pavel Exner
Copyright © 2011 Guido Schneider. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [5 citations]
The following is the list of published articles that have cited the current article.
- Christopher Chong, and Guido Schneider, “Numerical evidence for the validity of the NLS approximation in systems with a quasilinear quadratic nonlinearity,” Zamm-Zeitschrift Fur Angewandte Mathematik und Mechanik, vol. 93, no. 9, pp. 688–696, 2013.
- Hasibun Naher, Farah Aini Abdullah, and Syed Tauseef Mohyud-Din, “Extended generalized Riccati equation mapping method for the fifth-order Sawada-Kotera equation,” AIP Advances, vol. 3, no. 5, pp. 052104, 2013.
- I. S. Amiri, P. Naraei, and J. Ali, “Review and Theory of Optical Soliton Generation Used to Improve the Security and High Capacity of MRR and NRR Passive Systems,” Journal of Computational and Theoretical Nanoscience, vol. 11, no. 9, pp. 1875–1886, 2014.
- Martina Chirilus-Bruckner, Wolf-Patrick Düll, and Guido Schneider, “NLS approximation of time oscillatory long waves for equations with quasilinear quadratic terms,” Mathematische Nachrichten, 2014.
- Wolf-Patrick Duell, Alina Hermann, Guido Schneider, and Dominik Zimmermann, “Justification of the 2D NLS equation for a fourth order nonlinear wave equation - quadratic resonances do not matter much in case of analytic initial ,” Journal Of Mathematical Analysis And Applications, vol. 436, no. 2, pp. 847–867, 2016.