Gibbons–Tsarev equation (original) (raw)
The Gibbons–Tsarev equation is an integrable second order nonlinear partial differential equation. In its simplest form, in two dimensions, it may be written as follows: The equation arises in the theory of dispersionless integrable systems, as the condition that solutions of the Benney moment equations may be parametrised by only finitely many of their dependent variables, in this case 2 of them. It was first introduced by John Gibbons and Serguei Tsarev in 1996, This system was also derived, as a condition that two quadratic Hamiltonians should have vanishing Poisson bracket.
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| dbo:abstract | The Gibbons–Tsarev equation is an integrable second order nonlinear partial differential equation. In its simplest form, in two dimensions, it may be written as follows: The equation arises in the theory of dispersionless integrable systems, as the condition that solutions of the Benney moment equations may be parametrised by only finitely many of their dependent variables, in this case 2 of them. It was first introduced by John Gibbons and Serguei Tsarev in 1996, This system was also derived, as a condition that two quadratic Hamiltonians should have vanishing Poisson bracket. (en) 吉本斯-查理夫方程(Gibbons-Tsarev equation)是一个非线性偏微分方程： (zh) |
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| dct:subject | dbc:Nonlinear_partial_differential_equations |
| rdf:type | yago:WikicatNonlinearPartialDifferentialEquations yago:Abstraction100002137 yago:Communication100033020 yago:DifferentialEquation106670521 yago:Equation106669864 yago:MathematicalStatement106732169 yago:Message106598915 yago:PartialDifferentialEquation106670866 yago:Statement106722453 |
| rdfs:comment | The Gibbons–Tsarev equation is an integrable second order nonlinear partial differential equation. In its simplest form, in two dimensions, it may be written as follows: The equation arises in the theory of dispersionless integrable systems, as the condition that solutions of the Benney moment equations may be parametrised by only finitely many of their dependent variables, in this case 2 of them. It was first introduced by John Gibbons and Serguei Tsarev in 1996, This system was also derived, as a condition that two quadratic Hamiltonians should have vanishing Poisson bracket. (en) 吉本斯-查理夫方程(Gibbons-Tsarev equation)是一个非线性偏微分方程： (zh) |
| rdfs:label | Gibbons–Tsarev equation (en) 吉本斯-查理夫方程 (zh) |
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