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The stability of solutions of Vakhnenko’s equation. (English) Zbl 0809.35086

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.

MSC:

35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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