Consider the equation

$frac{partial{y}}{partial{t}}+yfrac{partial{y}}{partial{x}}=Gamma frac{partial^2y}{partial{x}^2}$

where $Gamma$ is a constant term.

Given that $y=frac{y_0}{2}-frac{y_0}{2}tanh(frac{x-ct}{L})$ satisfies the equation above, find $L$ and $c$ in terms of the constants $y_0$ or $Gamma$

My attempt:

$frac{partial{y}}{partial{x}}=frac{-y_0}{2L}sech^2(Phi)$ where $Phi=frac{x-ct}{L}$.

$frac{partial{y}}{partial{t}}=frac{y_0c}{2L}sech^2(Phi)$

$frac{partial^2{y}}{partial{x}^2}=frac{y_0}{L^2}sech^2(Phi)tanh(Phi)$

Hence plugging them into the equation above we get

$1-frac{y}{c}=Gamma frac{2}{cL}tanh(Phi)$, so $1-frac{y_0}{2c}=frac{4Gamma-y_0L}{2cL}tanh(Phi)$

What else should I do?