I'm looking at this second order quasilinear PDE:
$\alpha_{xx} - \alpha_{yy} - m\alpha^2 = 0$
Attempted Strategies:
- Fourier Transform resulted in convolution due to the $\alpha^2$ term, I don't think that would be pretty to work on.
- Separation of Variables resulted in not being able to separate the variables.
- I tried substituting $u=\alpha_x$ and $v=\alpha_y$ but I'm left with $(\int u_x dx)^2$ or $(\int u_y dy)^2$ in my equation afterwords due to substituting $u$ and $v$ back in, which seems like a dead end.
Do you guys have any suggestions for an analytical solution method?