THE VAKHNENKO EQUATION FROM THE VIEWPOINT OF THE INVERSE SCATTERING METHOD FOR THE KdV EQUATION

The formulation of the inverse scattering transform method is discussed for the nonlinear evolution equation (Ut + 'Uux)x + U = 0 (the Vakhnenko equation). It is shown that the equation system for the inverse scattering problem associated with the Vakhnenko equation can not contain the isospectral Schrodinger equation. The exact two soliton solutions are obtained by means of the use of elements of the inverse scattering problem for the KdV equation.