Lax pairs for the one-dimensional nonlinear evolutionary equation, and the generalized Miura transformation (Q1593923)
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scientific article; zbMATH DE number 1557277
| Language | Label | Description | Also known as |
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| English | Lax pairs for the one-dimensional nonlinear evolutionary equation, and the generalized Miura transformation |
scientific article; zbMATH DE number 1557277 |
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Lax pairs for the one-dimensional nonlinear evolutionary equation, and the generalized Miura transformation (English)
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28 January 2001
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It is well known that the Miura transformation connects solutions of the Korteweg-de Vries (KdV) equation to solutions of modified KdV equation. In this paper, the author proposes a generalized Miura map which connects the solutions of some generalized KdV equation to the solutions of some generalized mKdV equation. The reviewer feels that this is an interesting paper -- but it lacks geometry. As an example, Theorem 2 of this paper can be explained in a more geometric way, as shown by \textit{G. Wilson} [Phys. Lett. A 132, 445-450 (1988)].
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generalized Miura map
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Lax pair
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Korteweg-de Vries equation
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