Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

نویسندگان

چکیده

The mathematical description of localized solitons in the presence large-scale waves is a fundamental problem nonlinear science, with applications fluid dynamics, optics, and condensed matter physics. Here, evolution soliton as it interacts rarefaction wave or dispersive shock wave, examples slowly varying rapidly oscillating mean fields, for Korteweg–de Vries equation studied. Step boundary conditions give rise to either (step up) down). When one these can transmit through (tunnel) become embedded (trapped) inside, depending on its initial amplitude position. A topical review three separate analytical approaches undertaken describe interactions. First, basic perturbation theory introduced that found capture solution dynamics soliton–rarefaction interaction small dispersion limit. Next, multiphase Whitham modulation finite-gap are used soliton–dispersive Lastly, spectral an exact value obtained inverse scattering transform. For transmitted solitons, far-field asymptotics reveal phase shift type mentioned above. In trapped case, there no proper eigenvalue description, implying does not involve solution. These consistent, agree direct numerical simulation, accurately different aspects solitary wave–mean field interaction.

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ژورنال

عنوان ژورنال: Studies in Applied Mathematics

سال: 2023

ISSN: ['0022-2526', '1467-9590']

DOI: https://doi.org/10.1111/sapm.12615