On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations (Q1600489)
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scientific article; zbMATH DE number 1755370
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations |
scientific article; zbMATH DE number 1755370 |
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On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations (English)
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13 June 2002
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The authors present a direct and unifying scheme for the disclosure of bilinear Bäcklund transformations and linear Lax systems associated with the soliton equation. The scheme is based on a concept of scale invariance and on the use of a class of partitional polynomials: the binary Bell polynomials. In order to provide a complete picture of the method they start their discussions with the case of NLPDEs which can be derived from a quadratic Hirota equation, considering two simple examples: the KdV equation and the Sawada-Kotera equation.
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Hirota equation
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sine-Gordon equation
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modified KdV equation
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coupled ANS system
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bilinear Bäcklund transformations
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linear Lax systems
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soliton equation
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binary Bell polynomials
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KdV equation
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Sawada-Kotera equation
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