一类高阶Camassa-Holm方程的渐近行为

Asymptotic behavior for a class of higher-order Camassa-Holm equations

研究了一类高阶Camassa-Holm方程Cauchy问题,该类方程可以看作是Camassa-Holm方程的推广。讨论了该问题解的长时间行为。证明当|x|趋于无穷大、初始值为代数衰减时,该问题的解u(x,t)在无穷远处代数衰减的指标与初始值衰减指标相同。

The Cauchy problem,associated with a class of higher-order Camassa-Holm equations which can be regarded as a generalization of Camassa-Holm equation,is shown.The long-time behavior of the solutions for this problem is discussed.It is proved that the algebraic decay exponent of the solutions u(x,t)at infinity is the same as that of the initial value data when|x|tends to infinity and the initial value data are algebraic decay.