Abstract:
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 CamassaHolm 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 CamassaHolm equation and soliton surfaces. The first and second fundamental forms, surface area and
curvature for Camassa-Holm equation are found.
