High-order nonlinear Schrödinger equation for the envelope of slowly modulated gravity waves on the surface of finite-depth fluid and its quasi-soliton solutions

Ivan Gandzha 1 Yury Sedletsky 1 Denys Dutykh 2, *
* Auteur correspondant
1 Department of Theoretical Physics
2 LAMA - Laboratoire de Mathématiques
Abstract : We consider the high-order nonlinear Schrödinger equation derived earlier by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope of slowly modulated gravity waves on the surface of finite-depth irrotational, inviscid, and incompressible fluid with flat bottom. This equation takes into account the third-order dispersion and cubic nonlinear dispersive terms. We rewrite this equation in dimensionless form featuring only one dimensionless parameter kh, where k is the carrier wavenumber and h is the undisturbed fluid depth. We show that one-soliton solutions of the classical nonlinear Schrödinger equation are transformed into quasi-soliton solutions with slowly varying amplitude when the high-order terms are taken into consideration. These quasi-soliton solutions represent the secondary modulations of gravity waves.
Keywords : slow modulations Nonlinear Schrödinger equation multiple-scale expansions wave envelope gravity waves finite depth quasi-soliton
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Article dans une revue
Ukrainian Journal of Physics, 2014, 59 (12), pp.1201-1215. 〈http://ujp.bitp.kiev.ua/〉
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Contributeur : Denys Dutykh <>
Soumis le : lundi 16 février 2015 - 15:05:53
Dernière modification le : lundi 21 mars 2016 - 11:32:23

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Ivan Gandzha, Yury Sedletsky, Denys Dutykh. High-order nonlinear Schrödinger equation for the envelope of slowly modulated gravity waves on the surface of finite-depth fluid and its quasi-soliton solutions. Ukrainian Journal of Physics, 2014, 59 (12), pp.1201-1215. 〈http://ujp.bitp.kiev.ua/〉. 〈hal-01084747v3〉

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