Inverse Problem for the Wave Equation with a Polynomial Nonlinearity

Abstract: For the wave equation containing a nonlinearity in the form of anth order polynomial, we study the problem of determining the coefficients ofthe polynomial depending on the variable. We consider plane waves that propagate in a homogeneous medium in thedirection of a unit vector with a sharp front and incident on an inhomogeneity localized inside acertain ball. It is assumed that the solutions of the problems can be measured at thepoints of the boundary of this ball at the instants of time close to the arrival of the wavefront forall possible values of the vector. It is shown that the solution of the inverse problem is reduced to a series ofX-ray tomography problems. © Pleiades Publishing, Ltd. 2023.