论文标题
R-Camassa-Holm方程：平滑而奇异的解决方案
The r-Camassa-Holm equation: smooth and singular solutions
论文作者
论文摘要
本文介绍了R-Camassa-Holm（R-CH）方程，该方程描述了作用于由W1诱导的真实线上的二型差异的地理流动。保守的能量是针对问题的，由完整的W1，R Norm和for r = 2给出，我们恢复了Camassa-Holm方程。我们计算R-CH的谎言对称性，并研究各种对称性减少。我们引入了R> = 2的R-CH方程的奇异弱解，并在超过和正面碰撞中对其非线性相互作用的数值模拟中证明了它们的稳健性。关于R-CH弱奇异解决方案的未开发性能的一些开放问题，包括它们是否会从平滑的初始条件中出现。
This paper introduces the r-Camassa-Holm (r-CH) equation, which describes a geodesic flow on the manifold of diffeomorphisms acting on the real line induced by the W1,r metric. The conserved energy is for the problem is given by the full W1,r norm and the for r = 2, we recover the Camassa-Holm equation. We compute the Lie symmetries for r-CH and study various symmetry reductions. We introduce singular weak solutions of the r-CH equation for r >= 2 and demonstrates their robustness in numerical simulations of their nonlinear interactions in both overtaking and head-on collisions. Several open questions are formulated about the unexplored properties of the r-CH weak singular solutions, including the question of whether they would emerge from smooth initial conditions.
