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The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method. (English) Zbl 1067.37106
Summary: A Bäcklund transformation both in bilinear form and in ordinary form for the transformed Vakhnenko equation 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. The procedure is illustrated by considering the cases \(N=1\) and \(N=2\).

37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
Full Text: DOI
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