Geometric characteristics for Camassa-Holm equation

One of the actual problems of mathematical physics is to relate differential geometry and nonlinear differential equation. Research in this direction is very important, as the results are a theoretical and practical application. In this paper, we investigate the Camassa-Holm equation. It is well known that the integrable nonlinear Camassa-Holm equation play an important role in the study of wave propagation. We present the relationship between Camassa-Holm equation and soliton surfaces. The rst and second fundamental forms, surface area and curvature for Camassa-Holm equation are found.