A new loop algebra and the corresponding computing formula of constant \(\gamma \) in the quadratic-form identity, as well as the generalized Burgers hierarchy (Q1008081)
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scientific article; zbMATH DE number 5531551
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new loop algebra and the corresponding computing formula of constant \(\gamma \) in the quadratic-form identity, as well as the generalized Burgers hierarchy |
scientific article; zbMATH DE number 5531551 |
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A new loop algebra and the corresponding computing formula of constant \(\gamma \) in the quadratic-form identity, as well as the generalized Burgers hierarchy (English)
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24 March 2009
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A new loop algebra \(A\) is constructed in the context of an isospectral problem, whose compatability condition exhibits a zero-curvature equation \[ U_t - V_x + [U,V] = 0, \] where \(U,V \in A\). The new loop algebra contains four arbitrary constants. This algebra is applied to construct a new Liouville integrable hierarchy of evolution equations, which includes a generalized Burgers hierarchy. Bi-Hamiltonian structure of the new hierarchy is also found.
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Burgers hierarchy
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loop algebra
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zero-curvature equation
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bi-Hamiltonian structure
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