一个具有三次非线性项的可积两分量Camassa-Holm系统解的持久性

研究了一个具有三次非线性项的可积的两分量Camassa-Holm系统Cauchy问题解的持久性.通过用权函数估计的方法证明:如果两分量Camassa-Holm系统的初值以及初值的空间导数都以指数形式衰减,则两分量Camassa-Holm系统的强解也在无穷远处以指数形式衰减,进一步,给出了动量的最优衰减估计.

Persistence properties of solutions for an integrable two-component Camassa-Holm system with cubic nonlinearity

In this paper,we are concerned with the persistence properties of solutions of the Cauchy problem associated to an integrable two-component Camassa-Holm system with cubic nonlinearity.It is shown that a strong solution of the two-component Camassa-Holm system,initially decaying exponentially together with its spacial derivative,also decay exponentially at infinity by using weight functions.Furthermore,we give an optimal decaying estimate of the momentum.