Geometric characteristics for Camassa–Holm equation

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 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.