E.J. Parkes
Depart. Math., University of Strathclyde,
Richmond St., Glasgow G1 1XH, U.K.
e-mail: ejp@maths.strath.ac.uk

A novel nonlinear evolution equation integrable by the inverse scattering method

Abstract:
A Backlund transformation for an evolution equation (u_t+u u_x)_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.