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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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2011/854719 |
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| _version_ | 1850105309189636096 |
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| author | Guido Schneider |
| author_facet | Guido Schneider |
| author_sort | Guido Schneider |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-3cd6810c41a5483386a07e34fe88509e |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| 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 |