Parkes, E. J. The stability of solutions of Vakhnenko’s equation. (English) Zbl 0809.35086 J. Phys. A, Math. Gen. 26, No. 22, 6469-6475 (1993). Summary: Vakhnenko’s equation has two families of travelling wave solutions. The method of Rowlands and Infeld is used to investigate whether these solutions are stable to long wavelength perturbations of small amplitude. The method predicts stability for both families of solutions. Some comments on the validity of the method are given. Cited in 32 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction Keywords:travelling wave solutions; method of Rowlands and Infeld PDF BibTeX XML Cite \textit{E. J. Parkes}, J. Phys. A, Math. Gen. 26, No. 22, 6469--6475 (1993; Zbl 0809.35086) Full Text: DOI