Global weak solutions for a new periodic integrable equation with peakon solutions
Global weak solutions for a new periodic integrable equation with peakon solutions
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DOI：
10.1016/j.jfa.2003.07.010
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发表时间：
2004-07
影响因子：
1.7
通讯作者：
Z. Yin
中科院分区：
文献类型：
--
作者：
Z. Yin
最近，Degasperis和Procesi[18]研究了一类空间周期三阶色散偏微分方程，其中a， c0, c1， c2和c3是实常数。他们发现在这个族中只有三个方程满足渐近可积条件：KdV方程、Camassa-Holm方程和一个新方程。通过式（1.1）中的ºc2ºc3º0，我们发现了著名的Korteweg-de Vries方程，该方程描述了波浪在重力影响下在浅水自由表面的单向传播：u _ _ _ t， xfi表示平坦底部以上的波高，x与传播方向上的距离成正比，t与经过的时间成正比。KdV方程的柯西问题有
Recently, Degasperis and Procesi [18] studied the family of spatially periodic thirdorder dispersive partial differential equations ut c0ux guxxx¿ a2utxx º c1u2 c2u2 x c3uuxxfix, 1.1 fi where a, c0, c1, c2, and c3 are real constants. They found that there are only three equations that satisfy the asymptotic integrability condition within this family: the KdV equation, the Camassa–Holm equation and one new equation. With a º c2 º c3 º 0 in Eq.(1.1), we find the well-known Korteweg-de Vries equation which describes the unidirectional propagation of waves at the free surface of shallow water under the influence of gravity: u t, xfi represents the wave height above a flat bottom, x is proportional to distance in the direction of propagation and t is proportional to the elapsed time. The Cauchy problem of the KdV equation has