Abstract:
The coupled integrable dispersionless equations have a significant 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
R3, are studied. We obtain Gaussian and mean curvatures and also evaluate the area of
surface parametrically defined 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
field in three-dimensional Euclidean space.
