论文标题
在四阶非线性schrödinger方程中的高阶调制不稳定性
Higher-order modulation instability in a fourth-order Nonlinear Schrödinger Equation
论文作者
论文摘要
我们提供了四阶非线性schrödinger方程的高阶调制不稳定性的完整动力描述。对于该方程式的两只呼吸道溶液，我们已经在几何空间中确定了呼吸器的生长速率在参数空间相等的基因座。我们表明，一个圆圈界定了非线性schrödinger方程的整个参数空间。相比之下，它由相交圆和四阶方程的椭圆绑定。我们表明，对于非线性schrödinger方程层次结构中的所有高阶方程，参数空间遵循与四阶方程相似的几何解释。
We present a complete dynamical description of the higher-order modulation instability for a fourth-order nonlinear Schrödinger equation. For two-breather solutions of this equation, we have identified the locus in a geometrical space where the growth rates for the breathers are equal in parameter space. We show that a circle bounds the entire parameter space for the nonlinear Schrödinger equation. In contrast, it is bound by an intersecting circle and an ellipse for the fourth-order equation. We show that, for all the higher-order equations in the nonlinear Schrödinger equation hierarchy, the parameter space follows a similar geometric interpretation as for the fourth-order equation.
