Justification of the NLS Approximation for the KdV Equation Using the Miura Transformation

It is the purpose of this paper to give a simple proof of the fact that solutions of the KdV equation can be approximated via solutions of the NLS equation. The proof is based on an elimination of the quadratic terms of the KdV equation via the Miura transformation.

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Main Author: Guido Schneider
Format: Article
Language:English
Published: Wiley 2011-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2011/854719
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author Guido Schneider
author_facet Guido Schneider
author_sort Guido Schneider
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description It is the purpose of this paper to give a simple proof of the fact that solutions of the KdV equation can be approximated via solutions of the NLS equation. The proof is based on an elimination of the quadratic terms of the KdV equation via the Miura transformation.
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spelling doaj-art-3cd6810c41a5483386a07e34fe88509e2025-08-20T02:39:08ZengWileyAdvances in Mathematical Physics1687-91201687-91392011-01-01201110.1155/2011/854719854719Justification of the NLS Approximation for the KdV Equation Using the Miura TransformationGuido Schneider0IADM, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, GermanyIt is the purpose of this paper to give a simple proof of the fact that solutions of the KdV equation can be approximated via solutions of the NLS equation. The proof is based on an elimination of the quadratic terms of the KdV equation via the Miura transformation.http://dx.doi.org/10.1155/2011/854719
spellingShingle Guido Schneider
Justification of the NLS Approximation for the KdV Equation Using the Miura Transformation
Advances in Mathematical Physics
title Justification of the NLS Approximation for the KdV Equation Using the Miura Transformation
title_full Justification of the NLS Approximation for the KdV Equation Using the Miura Transformation
title_fullStr Justification of the NLS Approximation for the KdV Equation Using the Miura Transformation
title_full_unstemmed Justification of the NLS Approximation for the KdV Equation Using the Miura Transformation
title_short Justification of the NLS Approximation for the KdV Equation Using the Miura Transformation
title_sort justification of the nls approximation for the kdv equation using the miura transformation
url http://dx.doi.org/10.1155/2011/854719
work_keys_str_mv AT guidoschneider justificationofthenlsapproximationforthekdvequationusingthemiuratransformation