The main aim of this paper is to solve an inverse source problem for a general nonlinear hyperbolic equation. Combining the quasi-reversibility method and a suitable Carleman weight function, we define a map of which fixed point is the solution to the inverse problem. To find this fixed point, we define a recursive sequence with an arbitrary initial term by the same manner as in the classical proof of the contraction principle. Applying a Carleman estimate, we show that the sequence above converges to the desired solution with the exponential rate. Therefore, our new method can be considered as an analog of the contraction principle. We rigorously study the stability of our method with respect to noise. Numerical examples are presented.

翻译：本文的主要目的是解决一般非线性双曲线方程式的反源问题。 结合准反向法和适当的 Carleman 重量函数, 我们定义了一张地图, 其中的固定点是反向问题的解决办法。 为了找到这个固定点, 我们用与传统收缩原则证据相同的方式, 以任意的初始术语来定义循环序列。 应用 Carleman 估计, 我们显示上面的序列与指数率的预期解决方案一致。 因此, 我们的新方法可以被视为收缩原则的类比。 我们严格研究我们方法在噪音方面的稳定性, 提供了数字例子 。