Stability of Inverse Potential Problems for Nonlinear Wave Equations
The study of whether, and how continuously, an unknown coefficient (such as a potential) of a nonlinear wave equation can be reconstructed from measurements of the equation's response operator. Beyond uniqueness, the central question is stability: quantitative estimates bounding the error in the recovered coefficient by the error in the measured data, so that the inversion is well-posed. Techniques exploit the nonlinear interaction of waves and microlocal (symbol) analysis of the response operator.
2501.00748
This paper studies the inverse problem of recovering a lower-order potential coefficient in a wave equation with cubic nonlinearity from its nonlinear response (measurement) operator, and establishes…