The system of generalized Chaplygin gas equations with a coulomblike friction term has been investigated by using the famous Lie symmetry method. A direct and systematic algorithm based on the adjoint transformation and invariants of the admitted Lie algebras is then used to construct one‐ and two‐dimensional optimal system of the Chaplygin gas equations. Inequivalent classes of group invariant solutions are then obtained using the one‐dimensional optimal system. Further, the evolutionary behaviour of the weak discontinuity wave within the state characterized by one of the group invariant solutions is investigated in detail, and certain observations are noted in respect to their contrasting behaviour.

中文翻译：

---

具有源项的广义Chaplygin气体方程的对称性分析和最优系统

使用著名的李对称方法研究了具有库仑式摩擦项的广义Chaplygin气体方程组。然后使用直接的系统算法，基于伴随的李代数的伴随变换和不变量，来构建Chaplygin气体方程的一维和二维最优系统。然后使用一维最佳系统获得不等式的组不变解。此外，详细研究了弱不连续波在以一组不变解为特征的状态下的演化行为，并就它们的对比行为指出了某些观察结果。