Absorbing boundary conditions for nonlinear scalar partial differential equations

We present two strategies dealing with the design of absorbing boundary conditions for nonlinear scalar partial differential equations. The first one relies on the linearization of the equation and the second one relies on its paralinearization. We then introduce a finite volume scheme well-suited to our absorbing boundary conditions in the case of the semilinear wave equation. We finally present numerical experiments illustrating the efficiency of these methods in the case of semilinear wave equations and of nonlinear Schrödinger equations.