Problems for the Fermi–Pasta–Ulam (FPU) model for an inhomogeneous lattice

The oscillation equation for an inhomogeneous lattice is obtained within the FPU model. Based on it, we derive the generalized Korteweg-de Vries (KdV) type equation with a variable coefficient determined by the step of an inhomogeneous lattice. The inverse problems of recovering this coefficient by integrals of the solution to the equation are posed, investigated and solved. We have proved existence and uniqueness theorems of the solution to inverse problems. A series of computational experiments confirming the obtained theoretical results has been carried out. We present the results of the calculations in the form of computer images and graphs.