Nonlinear chiral modes in Bose-Einstein condensates with zero-energy and higher-order residual nonlinearities

The letter explores modulational instability (MI) in chiral Bose-Einstein condensates (BECs) using a modified Gross-Pitaevskii (GP) equation that includes a density-dependent gauge potential and residual higher-order interactions from shape-dependent confinement corrections. It shows that the interaction between current density and residual nonlinearity can cause instability when balanced with attractive two-body interactions. The growth rate of MI is determined, and the combined effects extend instability windows based on BEC density and wavenumber. Numerical simulations confirm analytical predictions, including the growth rate for single-wavelength perturbations and areas of instability with noisy initial conditions. The evolution and directional response of chiral solitons to residual nonlinearity are discussed, revealing shape-changing structures, breathing soliton trains, and rogue waves that are stabilized by adjusting the residual nonlinearity and MI onset. Findings suggest a way to manipulate MI in BECs using residual higher-order and current nonlinearities.