(untitled) (Contemporary Mathematics, 2024)
This study examines the generalized Schrödinger equation governing chiral solitons. We assess its integrability using the Painlevé test for nonlinear partial differential equations. Our analysis shows that the equation fails the Painlevé 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 Painlevé test. Therefore, we establish a general solution for this reduced equation, which we outline accordingly.