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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.

In this paper, we discuss the Lie symmetries, symmetry algebra and symmetry reductions of the equation which describes constant mean curvature surfaces via the generalized Weierstrass-Enneper formulae. First we point out that the equation admits an infinite-dimensional symmetry Lie algebra. Then using symmetry reductions, we obtain two integrable Hamiltonian systems (one autonomous, the other nonautonomous) with two degrees of freedom. The autonomous one was obtained by Konopelchenko and Taimanov by other means. Our method provides a new approach for construction of constant mean curvature surfaces.

Authors discover that a spacelike surface in Minkowski 3-space is related to a integrable system. They obtain a representation formula for spacelike surfaces with prescribed mean curvature. This representation formula is equivalent to that obtained by Akutagawa and Nishikawa.

In this paper, we obtain three types of Backlund transformations on surfaces with in three-dimensional Minkowski space , where and are principal curvatures, and l(>0) are arbitrary constants. Using these transformations, one can construct families of surfaces with in from known ones.

In this paper, we generalize the Backlund theorem on surfaces with Gaussian curvature K = −1 in R 3 to the surfaces with K = −1 in R 2,1.

It is well known that Backlund transformation is a powerful means in the study of nonlinear evolution equations. Up to now, a large number of works have been devoted to this aspect [1,2,3,4,5,6]. Recently, it is noticed that a unified explicit form of Backlund transformations can be obtained for some hierarchies of isospectral equations, such as Kdv, MKdv, Sine-Gordon and AKNS hierarchy [7–12]. The approach to the study is to construct the Darboux matrices first, and then prove the gauge equivalence of the related Lax pairs. However, to demonstrate the t part is quite difficult in this approach, and it is also hard to employ this method to study hierarchies of non-isospectral evolution equations.