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Advances in Mathematical Physics
Volume 2011 (2011), Article ID 854719, 4 pages
Research Article

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 [6 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. View at Publisher · View at Google Scholar
  • 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. View at Publisher · View at Google Scholar
  • 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. View at Publisher · View at Google Scholar
  • 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. View at Publisher · View at Google Scholar
  • 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. View at Publisher · View at Google Scholar
  • Wolf-Patrick Düll, “Justification of the Nonlinear Schrödinger Approximation for a Quasilinear Klein–Gordon Equation,” Communications in Mathematical Physics, 2017. View at Publisher · View at Google Scholar