Finding exact solutions to the two-dimensional eikonal equation

In this paper, the two-dimensional eikonal equation $f_x^2+f_y^2=\phi^2$, where $\phi=\frac1{v}$, and $v(x,y)$ is a wavespropagation velocity, is discussed. This non-linear equation is reduced to a quasilinear equation for a new dependent variable $u$. For some kinds of the functions $\phi$, solutions to the quasilinear equations are found. This means that it is possible to solve the original equation for such $\phi$. This paper also offers an approach to finding a new solution based on a known one.