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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

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.
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https://hal.archives-ouvertes.fr/hal-01084747
Contributor : Denys Dutykh <>
Submitted on : Monday, February 16, 2015 - 3:05:53 PM
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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. ⟨10.15407/ujpe59.12.1201⟩. ⟨hal-01084747v3⟩

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