Slowly varying envelope approximationについて．
Slowly varying envelope approximation - Wikipedia
\begin{aligned}
A(x+\lambda)
\simeq A(x) + \frac{\partial A}{\partial x}(x) \lambda
\end{aligned}
が成り立つとき，2次の項A(x+\lambda)
\simeq A(x) + \frac{\partial A}{\partial x}(x) \lambda
\end{aligned}
\begin{aligned}
\frac{1}{2}\frac{\partial^{2} A}{\partial x^{2}}(x) \lambda^{2}
\end{aligned}
は1次に比べて無視できる．つまり，\frac{1}{2}\frac{\partial^{2} A}{\partial x^{2}}(x) \lambda^{2}
\end{aligned}
\begin{aligned}
\Biggl| \frac{1}{2}\frac{\partial^{2} A}{\partial x^{2}}(x) \lambda^{2} \Biggr|
\ll \Biggl| \frac{\partial A}{\partial x}(x) \lambda \Biggr|.
\end{aligned}
\Biggl| \frac{1}{2}\frac{\partial^{2} A}{\partial x^{2}}(x) \lambda^{2} \Biggr|
\ll \Biggl| \frac{\partial A}{\partial x}(x) \lambda \Biggr|.
\end{aligned}
したがって，
\begin{aligned}
\Biggl| \frac{\partial^{2} A}{\partial x^{2}}(x) \Biggr|
\ll \Biggl| k \frac{\partial A}{\partial x}(x) \Biggr|.
\end{aligned}
\Biggl| \frac{\partial^{2} A}{\partial x^{2}}(x) \Biggr|
\ll \Biggl| k \frac{\partial A}{\partial x}(x) \Biggr|.
\end{aligned}
