The korteweg-de vries equation with small dispersion: Higher order lax-levermore theory
The korteweg-de vries equation with small dispersion: Higher order lax-levermore theory
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小色散的 korteweg-de vries 方程：高阶 lax-levermore 理论
DOI：
10.1002/cpa.3160430303
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发表时间：
1990
影响因子：
3
通讯作者：
S. Venakides
中科院分区：
文献类型：
--
作者：
S. Venakides
我们利用逆散射变换来研究在初值问题的解中出现的快速振荡：
$$\开始{聚集} {u_t} +6 u {u_x} + { \in ^2}{u_{xxx}} = 0，\hfill \\ u\left（{x，0} \right）= v\left（x \right），\hfill \end{聚集} $$
当∈ → 0.我们通过引入量子条件改进了Lax-Levermore理论，该理论给出了解的弱极限为∈ → 0。这使我们能够计算的波形的本地振荡的相移时，∈是小的。
We utilize the inverse scattering transformation to study the rapid oscillations which arise in the solution of the initial value problem:
$$\begin{gathered} {u_t} + 6u{u_x} + { \in ^2}{u_{xxx}} = 0, \hfill \\ u\left( {x,0} \right) = v\left( x \right), \hfill \\ \end{gathered} $$
when ∈ → 0. We refine the Lax-Levermore theory, which gives the weak limit of the solution as ∈ → 0, by introducing a quantum condition. This allows us to calculate the waveform of the local oscillations up to phase-shifts when ∈ is small.