A generalized Hirota-Satsuma coupled KdV system: Darboux transformations and reductions (Q2820927)
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scientific article; zbMATH DE number 6626355
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A generalized Hirota-Satsuma coupled KdV system: Darboux transformations and reductions |
scientific article; zbMATH DE number 6626355 |
Statements
A generalized Hirota-Satsuma coupled KdV system: Darboux transformations and reductions (English)
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12 September 2016
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Lax representation
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Darboux transformation
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Hirota-Satsuma KdV equation
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generalized Hirota-Satsuma coupled KdV system
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coupled Kadomtsev-Petviashvili equation
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soliton solution
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rational solution
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In this paper, the authors obtain a new Darboux transformation for the generalized Hirota-Satsuma coupled KdV (gHS-KdV) system from that for the coupled Kadomtsev-Petviashvili (cKP) equation through a reduction. The feature of this Darboux transformation is that it survives in the reductions of the gHS-KdV system to three integrable systems: the Hirota-Satsuma (HS)-KdV equation, the complex coupled KdV equation and the coupled KdV system. By iterating the Darboux transformation, the authors found the compact representations expressed as Gramm-type Pfaffians for the solutions to the gHS-KdV system. Moreover, they also obtained the solitons and rational solution of the gHS-KdV system by using the compact representations.
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