Starting from the Lax pairs, the nonlocal symmetries of the coupled variable-coefficient Newell-Whitehead system are obtained. By introducing an appropriate auxiliary dependent variable, the nonlocal symmetries are localized to Lie point symmetries and the coupled variable-coefficient Newell-Whitehead system is extended to an enlarged system with the auxiliary variable. Then the finite symmetry transformation for the prolonged system is found by solving the initial-value problems. Furthermore, by applying symmetry reduction method to the enlarged system, two kinds of the group invariant solutions are given.

中文翻译：

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耦合变系数 Newell-Whitehead 系统的非局部对称性和群不变解

从 Lax 对开始，得到耦合变系数 Newell-Whitehead 系统的非局部对称性。通过引入适当的辅助因变量，非局部对称性被局部化为李点对称性，耦合变量系数 Newell-Whitehead 系统被扩展为具有辅助变量的放大系统。然后通过求解初值问题，得到延展系统的有限对称变换。此外，通过对扩大后的系统应用对称约简方法，给出了两种群不变解。