论文标题
方程式AB家庭的非唯一性
Non-uniqueness for the ab-family of equations
论文作者
论文摘要
我们研究方程式的立方AB家庭，其中包括Fokas-Olver-Rosenau-Qiao（FORQ）和Novikov（NE）方程。对于$ a \ neq0 $，证明在Sobolev space $ h^s $，$ s <3/2 $中存在初始数据，并带有非唯一解决方案。通过研究2峰溶液的碰撞来构建多种溶液。此外，我们证明了新的现象，即对于该家庭的某些成员来说，即使“更快”的Pearmon位于“较慢”的Pearmon的前面，也可能发生2峰之间的碰撞。
We study the cubic ab-family of equations, which includes both the Fokas-Olver-Rosenau-Qiao (FORQ) and the Novikov (NE) equations. For $a\neq0$, it is proved that there exist initial data in the Sobolev space $H^s$, $s<3/2$, with non-unique solutions. Multiple solutions are constructed by studying the collision of 2-peakon solutions. Furthermore, we prove the novel phenomenon that for some members of the family, collision between 2-peakons can occur even if the "faster" peakon is in front of the "slower" peakon.
