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.
