The Korteweg–de Vries Equation, Posed in a Quarter-Plane

An initial- and boundary-value problem for the Korteweg–de Vries equation is shown to be well-posed. The considered problem may serve as a model for unidirectional propagation of plane waves generated by a wavemaker in a uniform medium. Such models apply in regimes in which nonlinear and dispersive effects are of comparable small order.