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A generalized Complex Ginzburg-Landau Equation: global existence and\n stability results

2019/05/21 by Simão Correia, Correia, Simão, Mário Figueira +1
Computer Science · Mathematics · Physics and Astronomy · #35B10 #35B35 #35Q56 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.1905.08521

openalex publication_date 2019/05/21 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We consider the complex Ginzburg-Landau equation with two pure-power\nnonlinearities and a damping term. After proving a general global existence\nresult, we focus on the existence and stability of several periodic orbits,\nnamely the trivial equilibrium, bound-states and solutions independent of the\nspatial variable. In particular, we construct bound-states either explicitly in\nthe real line or through a bifurcation argument for a double eigenvalue of the\nDirichlet-Laplace operator on bounded domains.\n

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