RESEARCH ARTICLE
Recurrent solutions of the linearly coupled complex cubic-quintic Ginzburg-Landau equations
Peng Gao,
Corresponding Author
Peng Gao
School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, P. R. China
Correspondence
Peng Gao, School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, P. R. China.
Email: [email protected]
Search for more papers by this authorPeng Gao,
Corresponding Author
Peng Gao
School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, P. R. China
Correspondence
Peng Gao, School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, P. R. China.
Email: [email protected]
Search for more papers by this authorAbstract
In this paper, we will establish the bounded solutions, periodic solutions, quasiperiodic solutions, almost periodic solutions, and almost automorphic solutions for linearly coupled complex cubic-quintic Ginzburg-Landau equations, under suitable conditions. The main difficulty is the nonlinear terms in the equations that are not Lipschitz-continuity, traditional methods cannot deal with the difficulty in our problem. We overcome this difficulty by the Galerkin approach, energy estimate method, and refined inequality technique.
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