论文标题
Camassa-Holm类型方程的持久性属性，$（n+1） - $订购非线性
Persistence properties of a Camassa-Holm type equation with $(n+1)-$order non-linearities
论文作者
论文摘要
获得了具有Camassa-Holm方程为特定成员的双曲线方程家族的低阶保护定律和对称性。我们表明该方程具有两个具有零秩序特征的保护定律，并且其对称性是由自变量和一定尺度的翻译产生的，并且研究了一些不变的解决方案。接下来，我们考虑考虑方程解的持久性和渐近性能。特别是，我们分析了方程解决方案对空间变量的大值的行为。我们表明，如果初始数据具有一定的渐近指数衰减，那么只要解决方案存在，这种属性就会持续存在。此外，根据大量空间变量值的初始数据的行为，如果在某个时候，解决方案具有相同的行为，则必须相同的消失。最后，我们证明了方程解决方案的独特延续结果。
Lower order conservation laws and symmetries of a family of hyperbolic equations having the Camassa-Holm equation as a particular member are obtained. We show that the equation has two conservation laws with zeroth order characteristics and that its symmetries are generated by translations in the independent variables and a certain scaling, as well as some invariant solutions are studied. Next, we consider persistence and asymptotic properties for the solutions of the equation considered. In particular, we analyse the behaviour of the solutions of the equation for large values of the spatial variable. We show that if the initial data has a certain asymptotic exponential decaying, then such property persists for any time as long as the solution exists. Moreover, depending on the behaviour of the initial data for large values of the spatial variable and if for some further time the solution shares the same behaviour, then it necessarily vanishes identically. Finally, we prove unique continuation results for the solutions of the equation.
