The linear dispersive relation of the travelling-wave solution is investigated for cubic G-L equation.Moreover,the relation among the parameter c0,the amplitude |u0|,and the most unstable wave number q is discussed.Then convergence of an unconditionally stable,explicit psendo-spectral scheme is proved by energy estimates.Finally,by using the proposed scheme,the chaotic attractor,bifurcation structure and asymptotic dynamics are obtained.The results show there exist two different types of chaotic attractors for the most unstable wave number q0 and was fixed the amplitude|u0| in the same one system.
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