一类非线性波动方程解的破裂与混沌

Blow-up and Chaos of the Solutions to a Category of Nonlinear Wave Equations

非线性波动方程是一类非线性发展方程,主要描述客观世界中具有波动形态的随时间变化的事物·在此类方程中,因其所描述的对象多数具有发展轨迹间断及轨迹混沌的特点,故其动力学性态一般蕴涵有破裂及混沌·主要分析了一类带有防爆因子非线性波动方程解的形态,研究了此类方程解的破裂问题,运用逼近论方法,给出了解发生间断的条件·利用间断解的特点,分析其间断点处的性态,根据Li Yorke定理,证明了在一定条件下间断解在其间断点处的混沌现象·

The nonlinear wave equations are a category of nonlinear evolution equations describing mainly the things changing with time and having waved shape. Because most of these equations feature the interruption and chaos of their evolution traces in solution, their dynamics states contain blowup and chaos in general. The state of a category of nonlinear wave equations with preventable blowup factor and the blowup problem of the solutions to these equations are studied. By way of approximation, the conditions of interruption occurrence are given. With the interruptive solutions discussed, the state at their interrupting point is analyzed. The chaos phenomenon is verified at the interrupting point of the interruptive solutions under certain conditions, according to the LiYorke theorem.