In this paper, symmetry groups of a two-dimensional weakly singular integral equation are discussed. A new method is proposed for the prolongation formula of the given equations. Using the introduced prolongation formula, we derive the symmetry groups and invariant solutions of the above-mentioned weakly singular integral equation wherever possible. In order to solve the extracted determining equation, a special approach is proposed. The symmetry groups for different types of the free terms are presented.

中文翻译：

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二维弱奇异积分方程的李对称性分析

本文讨论了二维弱奇异积分方程的对称群。针对给定方程的延长公式提出了一种新方法。利用引入的延拓公式，我们尽可能推导出上述弱奇异积分方程的对称群和不变解。为了求解提取的确定方程，提出了一种特殊的方法。给出了不同类型自由项的对称群。