Analysis of a Galerkin approach applied to a system of coupled Schrödinger equations

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• 作者：Luisa Fernanda Vargas ; Juan Carlos Muñ ; oz Grajales ; ^{jcarlmz@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35Q60 ; 65M12 ; 65T50 ; 65M70
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：318-342
• 全文大小：600 K

文摘

We study error and convergence rate of a fully discrete Fourier–Galerkin scheme to approximate the solutions of a system consisting of two coupled cubic Schrödinger equations with cross modulation, which is a model for the propagation of a nonlinear pulse in a linearly birefringent Kerr optical fiber. We also establish a result on existence and uniqueness of a solution of the corresponding initial value problem.