Exact Traveling Wave Solutions of Time-Dependent Ginzburg-Landau Theory for Atomic Fermi Gases Near the BCS-BEC Crossover

This paper studied the exact traveling wave solutions of time-dependent Ginzburg-Landau (TDGL) theory for atomic fermi gases near the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCS-BEC) crossover. When g = 0, we utilize the Jacobi elliptic function expansion method and homogeneous balance method to obtain some exact traveling wave solutions, including some envelop solitary wave solutions; since \(g\not=0\), we introduce an auxiliary function to get some exact traveling wave solutions under the condition that d is a complex, and a numerical result is provided in the end.