短脉冲方程的周期波的波长

The Wave Length of Periodic Waves of a Short Pulse Equation

主要研究含参数短脉冲方程的周期波的波长.通过变量变换,短脉冲方程可以转化为一个平面多项式微分系统.当参数α<0时,短脉冲方程具有光滑的周期波,利用动力系统的定性理论和分析的方法研究这个多项式微分系统,其主要结果是给出周期函数T(h)的单调性质.结果表明,周期函数T(h)的单调性受参数β符号的影响.

The wave length of periodic waves of a short pulse equation with parameters is studied.The short pulse equation is transformed into a plane polynomial differential system through variable transformation.When the parameterα<0,the short pulse equation has a smooth periodic wave.The qualitative theory and analysis on dynamical systems are used to study this polynomial differential system.The main result is the monotonicity of T(h),which is affected by the parameterβ.