Abstract
Abstract It is shown that two classes of n-component mKdV equations are Painleve integrable, and the resonances occur, respectively, at −1,3,4, 0,…,0 n−1 , 1,…,1 n−1 , 5,…,5 n−1 for the geometric n-component mKdV equation which arises from curve motions in Euclidean space, and −1,3,4, 0,…,0 n−1 , 2,…,2 n−1 , 4,…,4 n−1 for another n-component mKdV equation which has an infinite number of Lie Backlund symmetries. It is also shown that the two-component geometric mKdV equation admits an infinite number of conservation laws. Conservation laws for several systems are constructed.
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