Hopf bifurcations of traveling wave solutions for time-dependent Ginzburg–Landau equation for atomic Fermi gases near the BCS-BEC crossover

This paper studied the traveling wave solutions for the time-dependent Ginzburg–Landau equation for atomic Fermi gases near the BCS-BEC crossover, and proposed the parameter conditions that appear the Hopf bifurcations when g=0g=0 and g≠0. Under these parameter conditions, by numerical simulations, we gained the diagram of the periodic traveling wave solutions and their phase diagram, and we can know the velocity’s range that appear Hopf bifurcation is 1.97⩽e⩽9.311.97⩽e⩽9.31.

► We studied the traveling wave solutions for the TDGL equation.
► We proposed the parameter conditions that the Hopf bifurcations appear when g=0g=0 and g≠0.
► We gave the numerical simulation of the theoretical results when g=0g=0 and g≠0.
► We obtained the phase diagram of the periodic traveling wave solutions.
► We gave out the velocity’s range that guarantees Hopf bifurcation appear is 1.97⩽e⩽9.311.97⩽e⩽9.31.