Links between \((\gamma_n, \sigma_k)\)-KP hierarchy, \((\gamma_n, \sigma_k)\)-mKP hierarchy, and \((2+1)-(\gamma_n, \sigma_k)\)-Harry Dym hierarchy (Q277722)
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scientific article; zbMATH DE number 6575723
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Links between \((\gamma_n, \sigma_k)\)-KP hierarchy, \((\gamma_n, \sigma_k)\)-mKP hierarchy, and \((2+1)-(\gamma_n, \sigma_k)\)-Harry Dym hierarchy |
scientific article; zbMATH DE number 6575723 |
Statements
Links between \((\gamma_n, \sigma_k)\)-KP hierarchy, \((\gamma_n, \sigma_k)\)-mKP hierarchy, and \((2+1)-(\gamma_n, \sigma_k)\)-Harry Dym hierarchy (English)
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2 May 2016
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Summary: The new (2+1)-\((\gamma_n, \sigma_k)\)-Harry Dym hierarchy and \((\gamma_n, \sigma_k)\)-mKP hierarchy with two new time series \(\gamma_n\) and \(\sigma_k\), which consist of \(\gamma_n\)-flow, \(\sigma_k\)-flow, and mixed \(\gamma_n\) and \(\sigma_k\) evolution equations of eigenfunctions, are proposed. Gauge transformations and reciprocal transformations between \((\gamma_n, \sigma_k)\)-KP hierarchy, \((\gamma_n, \sigma_k)\)-mKP hierarchy, and (2+1)-\((\gamma_n, \sigma_k)\)-Harry Dym hierarchy are studied. Their soliton solutions are presented.
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soliton hierarchies
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KdV equation
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0.8552823
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0.8504114
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0.84777874
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0.84472436
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0.8426791
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0.84226036
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0.84170187
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