Abstract
In this paper, a multi-component combined short pulse-mKdV equation is constructed as a nonstreching invariant curve flow in the n-dimensional unit sphere Sn(1)=SO(n+1)/SO(n). The invariant subspace method is used to solve the resulting combined short pulse-mKdV equation with n = 1. Through symbolic computation with the aid of mathematical software Maple, new exact solutions are obtained from its two-dimensional invariant subspaces formed in forms of the exponential functions and trigonometric functions.