广义河床流体模型方程单调递减扭状孤波解的渐近稳定性

Asymptotic stability of the monotone decreasing kink profile solitary-wave solution for generalized river-bed model equation

研究了广义河床流体模型方程单调递减扭状孤波解的渐近稳定性。首先运用平面动力系统的理论和方法证明了该方程扭状孤波解的存在性;其次证明了该单调递减扭状孤波解具有的3个性质,特别是给出了该行波解的一阶和二阶导数估计式;最后运用反导数方法、先验估计方法和Young不等式,证明了该模型方程单调递减扭状孤波解是渐近稳定的。

The asymptotic stability of monotone decreasing kink profile solitary-wave solution for generalized river-bed model equation was mainly studied.Firstly,by using the theory of planar dynamical system,the existence of kink profile solitary-wave solution of this equation was proved.Secondly,three properties of the monotone decreasing kink profile solitary-wave solution were proved,especially the first-order and second-order derivative estimation formulas of this traveling wave solution were given.Finally,by using anti-derivative strategy,with the help of priori estimate and Young inequality,it was proved that the monotone decreasing kink profile solitary-wave solution of model equation was asymptotically stable.