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.
Domains
Fluid mechanics [physics.class-ph] Fluid Dynamics [physics.flu-dyn] Atmospheric and Oceanic Physics [physics.ao-ph] Computational Physics [physics.comp-ph] Numerical Analysis [math.NA] Analysis of PDEs [math.AP] Pattern Formation and Solitons [nlin.PS] Exactly Solvable and Integrable Systems [nlin.SI]Origin | Publisher files allowed on an open archive |
---|