A novel nonlinear evolution equation integrable by the inverse scattering method

Vakhnenko, V.O. and Parkes, E.J.; Nikitin, A.G. and Boyko, V.M. and Popovych, R.O., eds. (2002) A novel nonlinear evolution equation integrable by the inverse scattering method. In: Proceedings of the Fourth International Conference, Symmetry in Nonlinear Mathematical Physics. Proceedings of Institute of Mathematics of NAS of Ukraine, 43 . Institute of Mathematics of NAS, UKR, pp. 384-391. ISBN 9660224869 (http://www.imath.kiev.ua/~symmetry/Symmetry2001/Va...)

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Abstract

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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