By -soliton solutions and a velocity resonance mechanism, soliton molecules are constructed for the KdV-Sawada-Kotera-Ramani (KSKR) equation, which is used to simulate the resonances of solitons in one-dimensional space. An asymmetric soliton can be formed by adjusting the distance between two solitons of soliton molecule to small enough. The interactions among multiple soliton molecules for the equation are elastic. Then, full symmetry group is derived for the KSKR equation by the symmetry group direct method. From the full symmetry group, a general group invariant solution can be obtained from a known solution.

中文翻译：

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KdV-Sawada-Kotera-Ramani方程的孤子分子和完全对称群

通过-孤子解和速度共振机构，孤子分子构建的KDV-泽田-阶KdV-拉马尼（KSKR）方程，这是用来模拟孤子的共振在一维空间。通过将两个孤子分子的孤子之间的距离调整到足够小，可以形成不对称孤子。该方程的多个孤子分子之间的相互作用是弹性的。然后，采用对称群直接法导出了KSKR方程的完全对称群。从完全对称组中，可以从已知解中获得一般组不变解。