Vakhnenko, V.O. and Parkes, E.J. (2002) A novel nonlinear evolution equation integrable by the inverse scattering method. [Proceedings Paper]
A Backlund transformation for an evolution equation (ut+u ux)x+u=0 transformed into new coordinates is derived. An inverse scattering problem is formulated. The inverse scattering method has a third order eigenvalue problem. A procedure for finding the exact N-soliton solution of the Vakhnenko equation via the inverse scattering method is described.
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