Abstract <p>The oscillation equation for an inhomogeneous lattice is obtained within the Fermi–Pasta–Ulam (FPU) model. Based on it, a generalized Korteweg–de Vries (KdV)-type equation with a variable coefficient, determined by the step of an inhomogeneous lattice, is derived. Inverse problems of recovering this coefficient by integrals of the solution to the equation are posed, investigated, and solved. Theorems on the existence and uniqueness of solutions to inverse problems are proved. A series of computational experiments confirming the obtained theoretical results are carried out. The results of the calculations in the form of computer images and graphs are presented.</p>