Integrability of the modified generalised Vakhnenko equation (Q2872442)

The authors of the paper under review investigate various properties of the modified generalised Vakhnenko equation (mGVE) presented in [\textit{A. J. Morrison} and \textit{E. J. Parkes}, Chaos, Solitons, Fractals, 16, 13 (2001)]. This equation can be transformed into the Vakhnenko equation, which describes the propagation of shortwave perturbations in a relaxing medium [\textit{V. O. Vakhnenko}, J. Math. Phys. 40, No. 4, 2011--2020 (1999; Zbl 0946.35094)].NEWLINENEWLINECombining the Bell polynomials approach and the Hirota direct method, they construct \(N\)-soliton solutions and quasiperiodic solutions, and present the bilinear formalism, the bilinear Bäcklund transformations, the Lax pairs and the conservation laws for mGVE. At the end, an asymptotic property of one-periodic wave solutions is discussed.