Korteweg–de Vries dynamics at the edge of a composite boson liquid
Phys. Rev. B 114, 084505 – Published 17 August, 2026
DOI: https://doi.org/10.1103/5s1b-3ssb
Abstract
In this work, we show that the edge dynamics of the composite boson condensate in the weakly nonlinear regime is governed by the Korteweg–de Vries (KdV) equation. Our starting point is the Chern-Simons-Ginzburg-Landau (CSGL) theory in the lower half-plane, where the effective edge dynamics are encoded in anomaly-compatible boundary conditions. The CSGL theory captures several key features of the Laughlin state. The saddle-point bulk dynamics and the corresponding boundary conditions of this action can be reformulated as two-dimensional compressible fluid dynamic equations, subject to a quantum Hall constraint that links the superfluid vorticity to its density fluctuations. The boundary conditions in this hydrodynamic framework consist of no-penetration and no-stress conditions. We then apply the method of multiple scales to this hydrodynamic system and derive the KdV equation for the edge dynamics in the weakly nonlinear regime. By employing the Hamiltonian framework for the KdV equation, we show that we can recover the chiral Luttinger liquid theory in the linearized regime and provide a pathway for canonically quantizing the edge dynamics in the weakly nonlinear limit.
