The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations

We develop an efficient and convergent numerical method for solving the inverse problem of determining potential nonlinear hyperbolic equations from lateral Cauchy data. In our we construct a sequence linear problems whose corresponding solutions converge to function that can be used efficiently compute approximate solution interest. The convergence analysis is established by combining contraction principle Carleman estimates. numerically solve using quasi-reversibility method. Numerical examples are presented illustrate efficiency