Soliton surfaces associated with the (1+1)- dimensional Yajima-Oikawa equation

Abstract

Soliton surfaces associated with integrable systems play a significant role in physics and mathematics. In this paper, we investigate the relationship between integrable equations and differential geometry of surface by the example of the Yajima-Oikawa equation. The integrability of nonlinear equations is understood as the existence their Lax representations. Using the connection between classical geometry and soliton theory, we have found the soliton surface related with the Yajima-Oikawa equation. The surface area, curvature, the first and second fundamental forms are found. Soliton surfaces associated with integrable systems play a significant role in physics and mathematics. In this paper, we investigate the relationship between integrable equations and differential geometry of surface by the example of the Yajima-Oikawa equation. The integrability of nonlinear equations is understood as the existence their Lax representations. Using the connection between classical geometry and soliton theory, we have found the soliton surface related with the Yajima-Oikawa equation. The surface area, curvature, the first and second fundamental forms are found.