General Lax-representation of a new higher-dimensional system: The current-fed membrane

In this paper, we delve into the prolongation structure of a coupled dispersionless system within the viewpoint of Wahlquist–Estabrook’s approach. Paying particular attention to the special linear SL(2,R)SL(2,R)-symmetry of the system, we derive the more general Lax-pairs of a new higher-dimensional system stemming from the generalization of the Morris’s formalism geared towards constructing some family of nonlinear partial differential evolution model equations with additional spatial dimensions. Looking forward to providing a physical meaning of the new equations, we investigate the dynamics of a current-fed membrane within an external magnetic field and submitted to an additional constraint.