2阶Camassa-Holm方程行波解附近的解的衰减性

The Decay Property of Solutions Near the Traveling Waves for the Second-Order Camassa-Holm Equation

该文研究2阶Camassa-Holm(CH)方程Cauchy问题在行波附近的解的衰减性.采用Y.Martel等在研究临界广义Korteweg-de Vries(KdV)方程的孤立子的稳定性时所用的伪共形变换方法,研究了具有指数衰减初值的解,得到解可被衰减的指数函数控制.

The decay properties of solutions around the traveling waves for Cauchy problem of the second-order Camassa-Holm(CH)equation is studied.Applying the extended pseudo-conformal transformation methods that appear the relevant works on the generalized Korteweg-de Vries equation(KdV)from Martel and Merle,the solution is controlled by the decaying function with exponential speed,corresponding to the initial data and its second derivative with exponential decay.