[微積] anharmonic oscillator, linear system

[HJpower (くま)]

My problem and my concerned issue are written in the following link:

https://math.stackexchange.com/questions/2423108/anharmonic-oscillator-with-nonlinear-term-solution


Question:

How to solve d^2x/dt^2 + w_0^2*x + a*x^3=0

,with the initial conditions: x(t_n)=x_n, and p(t_n)=p_n?



The solution should be one of the Jacobi elliptic functions, or the

combination of them.




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→ Vulpix      : Try to do some scaling to get the standard ODE?
→ wohtp       : 你貼的連結裡面的連結不是都公式寫好好了嗎
→ Vulpix      : 如果你的a是正的，試試看湊成cn的方程吧。