# How to use matlab to solve this non-linear equations？

$$\begin{cases} m_d=m+k_1m(m^2+n^2)+k_2m(m^2+n^2)^2 \\ n_d=n+k_1n(m^2+n^2)+k_2n(m^2+n^2)^2 \end{cases}$$

Now have these two linear equations, I need to calculate $m$ and $n$ from $m_d$ and $n_d$, other parameters is know, how to do it, if it's linear equations, I can do it, but now is non-linear, It seemed no idea for it , does anyone can provide details of solving and thinking?

If you properly factor the two equations and compute the ratio, you end with $$\frac{m_d}{n_d}=\frac m n$$ So $$m=\frac{m_d}{n_d} n$$ Replace $m$ in any of the equations to get a polynomial in $n$.