Ablowitz-Kaup-Newell-Segur system, conservation laws and Backlund transformation of a variable-coefficient Korteweg-de Vries equation in plasma physics, fluid dynamics or atmospheric science

摘要

For a variable-coefficient Korteweg-de Vries equation in a lake/sea, two-layer liquid, atmospheric flow, cylindrical plasma or interactionless plasma, in this paper, we derive the bilinear Backlund transformation, non-isospectral Ablowitz-Kaup-Newell-Segur system and infinite conservation laws for the wave amplitude under certain constraints among the external force, dissipation, nonlinearity, dispersion and perturbation.