On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: Universality of critical behaviour
On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: Universality of critical behaviour
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DOI：
10.1007/s00220-006-0021-5
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发表时间：
2006-10-01
影响因子：
2.4
通讯作者：
Dubrovin, Boris
中科院分区：
文献类型：
--
作者：
Dubrovin, Boris
研究了最简单双曲方程u (t) + a(u) u (x) = 0的哈密顿摄动。我们认为，非扰动方程的梯度突变点附近的扰动方程解的行为本质上与一般扰动的选择无关，与一般解的选择无关。此外，还用可积四阶ODE的一个特殊解描述了这种行为。
Hamiltonian perturbations of the simplest hyperbolic equation u (t) + a(u) u (x) = 0 are studied. We argue that the behaviour of solutions to the perturbed equation near the point of gradient catastrophe of the unperturbed one should be essentially independent on the choice of generic perturbation neither on the choice of generic solution. Moreover, this behaviour is described by a special solution to an integrable fourth order ODE.