Soliton surfaces induced by the coupled integrable dispersionless equation with self-consistent sources

The coupled integrable dispersionless equations have a signi cant interest because of structure, integrability, and the possibility of obtaining a soliton solution. In this paper, we construct soliton surfaces for integrable dispersionless equation with self-consistent sources in Riemann space. The surfaces, arising from M-XXXII equation and their reduction in R ³, are studied. We obtain Gaussian and mean curvatures and also evaluate the area of surface parametrically de ned with the Riemannian metric. Using the scale transformation and transformation of dependent and independent variables of the coupled dispersionless equations we obtain the equation that describes a current-fed string interacting with an external magnetic eld in three-dimensional Euclidean space. (paper)