In this paper, the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2.1. Using this transformation, families of surfaces with constant mean curvature from known ones can be constructed.
Taking the potential fifth-order MKdV equation as an example to introduce a possible way to construct invariance of a nonlinear PDE. Based on an obtained Backlund transformation of the potential fifth-order MKdV equation and by solving the corresponding Ricatti form Lax pairs, an invariance of the potential fifth-order MKdV equation is digged out. Thus, just by differential and quadrature procedure,the solutions of the potential fifth-order MKdV equation can be obtained from a known solution.
