求等价群的代数方法
Algebraic method for finding equivalence groups
摘要：
将计算微分方程组的完全点对称群的代数方法推广到求一类微分方程组的完全等价群。扩展的方法使用相应的等价代数的知识。两个版本的方法，其中第一个涉及的自同构群的代数和第二个是基于其megaideals的列表。我们说明了基于megaideal的版本的方法与计算的完全等价群的一类非线性波方程的应用在非线性弹性。
英文摘要：
The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the corresponding equivalence algebra. Two versions of the method are presented, where the first involves the automorphism group of this algebra and the second is based on a list of its megaideals. We illustrate the megaideal-based version of the method with the computation of the complete equivalence group of a class of nonlinear wave equations with applications in nonlinear elasticity.
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