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We develop an efficient and convergent numerical method for solving theinverse problem of determining the potential of nonlinear hyperbolic equationsfrom lateral Cauchy data. In our numerical method we construct a sequence oflinear Cauchy problems whose corresponding solutions converge to a functionthat can be used to efficiently compute an approximate solution to the inverseproblem of interest. The convergence analysis is established by combining thecontraction principle and Carleman estimates. We numerically solve the linearCauchy problems using a quasi-reversibility method. Numerical examples arepresented to illustrate the efficiency of the method.

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