I am wondering if the PDE $u_{t}+u^2u_x=\sin(u)$ is homogeneous.
The constant $u=0$ satisfies the equation so I think it is homogeneous? There does seem to be other definitions of homogeneity online that I’ve not encountered, such as every multiple of a solution is also a solution, so I am not clear on this? Also would the equation be classed as 'Non-linear' or 'Quasi-linear'?
In this thread we have the definition that if $u$ is a solution then $\alpha u$ must be a solution.
In this thread in the 4th example, this definition wouldn’t hold, but it is said to be homogeneous.
This is where there is confusion.