The standard wave equation in two dimensions takes the form

\[u_{tt} = u_{xx}+u_{yy} \]

It is a challenging task to construct a wave equation for which waves travel in one direction only. One possibility is the equation

\[u_{xt} = u_{tt}-\frac{1}{2}u_{yy} \]

What possible boundary conditions would arise from physical considerations?

Google: Wave equation, linear, absorbing boundaries, dispersion relation, one-way wave equation, Engquist & Majda

Challenges: 3 dimensions (2 space, 1 time), applications