On the Global Behavior of Solutions of a Coupled System of Nonlinear Schrödinger Equation

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• 作者：Edè ; s Destyl ; Sylvere Paul Nuiro and Pascal Poullet
• 刊名：Studies in Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：138
• 期：2
• 页码：227-244
• 全文大小：503K
• ISSN：1467-9590

文摘

We mainly study a system of two coupled nonlinear Schrödinger equations where one equation includes gain and the other one includes losses. This model constitutes a generalization of the model of pulse propagation in birefringent optical fibers. We aim in this study at partially answering a question of some authors in [1]: “Is the H¹-norm of the solution globally bounded in the Manakov case, when γ<κ ?” We found that in the Manakov case, and when γ<κ, the solution stays in L2(0,T;H1), and also that the H¹-norm of the solution cannot blow up in finite time. In the Manakov case, an estimate of the total energy is provided, which is different from that has been given in [1]. These results are corroborated by numerical results that have been obtained with a finite element solver well adapted for that purpose.