Absorbing boundary conditions for the stationary forced KdV equation

In the present work, we study the stationary Korteweg–de Vries (KdV) equation with a forcing for a flow of an inviscid and incompressible fluid. The stationary fKdV equation is defined in an infinite domain and it is reduced to a bounded domain by introducing absorbing boundary conditions. A new numerical method is proposed to solve this boundary value problem. New multiple numerical solitary wave solutions of the stationary KdV equation are discussed for various forcings. Numerical examples are provided to confirm and illustrate the accuracy and effectiveness of the method.