Ablowitz–Kaup–Newell–Segur system, conservation laws and Bäcklund transformation of a variable-coefficient Korteweg–de Vries equation in plasma physics, fluid dynamics or atmospheric science
Yu-Qi Chen, Bo Tian, Qi‐Xing Qu, He Li, Xue-Hui Zhao, He‐Yuan Tian, Meng Wang
Abstract
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 Bäcklund 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.
Topics & Concepts
Conservation lawPhysicsKorteweg–de Vries equationMathematical physicsIsospectralTransformation (genetics)Nonlinear systemPerturbation (astronomy)DissipationClassical mechanicsThermodynamicsQuantum mechanicsChemistryGeneBiochemistryNonlinear Waves and SolitonsNonlinear Photonic SystemsAdvanced Mathematical Physics Problems