Some Weak Self‐adjoint Forced KdV Equations

The Korteweg‐de Vries equation with a forcing term is established by recent studies as a simple mathematical model of describing the physics of a shallow layer of fluid subject to external forcing. It serves as an analytical model of tsunami generation by submarine landslides. One of the present authors has generalized the concept of quasi self‐adjoint equations by introducing the definition of weak self‐adjoint equations. In this paper we find a class of weak self‐adjoint forced Korteweg‐de Vries equations. By using a general theorem on conservation laws proved in [10] and the property of weak self‐adjointness [4], we find conservation laws for a forced Korteweg‐de Vries equation.