Quasiclassical integrability condition in AKNS scheme
arXiv:2308.12518 · doi:10.1016/j.physd.2024.134085
Abstract
In this paper, we study the condition of quasiclassical integrability of soliton equations. This condition states that the Hamiltonian structure of equations, which govern propagation of high-frequency wave packets, is preserved by the dispersionless flow independently of initial conditions. If this condition is fulfilled, then the carrier wave number of any packet is a certain function of local values of the dispersionless variables pertained to the soliton equations under consideration. We show for several examples that this function together with the dispersion relation for linear harmonic waves determine the quasiclassical limit of the Lax pair functions in the scalar representation of the Ablowitz-Kaup-Newell-Segur scheme.
arXiv comment8 pages
References in corpus (12)
- The theory of optical dispersive shock waves in photorefractive media
- Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory
- Breaking of Galilean invariance in the hydrodynamic formulation of ferromagnetic thin films
- On Whitham theory for perturbed integrable equations
- Gurevich-Pitaevskii problem and its development
- Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate
- Dispersive hydrodynamics of nonlinear polarization waves in two-component Bose-Einstein condensates
- Theory of quasi-simple dispersive shock waves and number of solitons evolved from a nonlinear pulse
- Asymptotic theory of not completely integrable soliton equations
- Solitary wave fission of a large disturbance in a viscous fluid conduit
- Propagation of wave packets along large-scale background waves
- Number of solitons produced from a large initial pulse in the generalized NLS dispersive hydrodynamics theory