Inverse problem for the Boussinesq–Love equation

For an abstract, high-order, incomplete Sobolev-type equation, an inverse problem with final redefinition is considered. Conditions for the unique solvability of the problem are found. Some special cases are considered. The main result contains necessary and sufficient conditions for the existence and uniqueness of a solution of the inverse problem for high-order, Sobolev-type equations. This technique is applied to the study of the inverse problem for the Boussinesq–Love equation.