Painlevé Analysis and Chiral Solitons from Quantum Hall Effect

This study examines the generalized Schr & ouml;dinger equation governing chiral solitons. We assess its integrability using the Painlev & eacute; test for nonlinear partial differential equations. Our analysis shows that the equation fails the Painlev & eacute; test, suggesting the Cauchy problem cannot be solved using the inverse scattering transform. However, through a traveling wave reduction, we find that the resulting nonlinear ordinary differential equation does satisfy the Painlev & eacute; test. Therefore, we establish a general solution for this reduced equation, which we outline accordingly.