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A generalized complex Ginzburg-Landau equation: Global existence and stability results

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    * Corresponding author 
The first author is supported by Fundação para a Ciência e Tecnologia, through the grant UIDB/MAT/04459/2020. The second author is supported by Fundação para a Ciência e Tecnologia, through the grant UIDB/04561/2020
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  • We consider the complex Ginzburg-Landau equation with two pure-power nonlinearities and a damping term. After proving a general global existence result, we focus on the existence and stability of several periodic orbits, namely the trivial equilibrium, bound-states and solutions independent of the spatial variable. In particular, we construct bound-states either explicitly in the real line or through a bifurcation argument for a double eigenvalue of the Dirichlet-Laplace operator on bounded domains.

    Mathematics Subject Classification: Primary: 35Q56, 35B10, 35B35.

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