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Spike-Layer Simulation for Steady-State Coupled Schrödinger Equations

Published online by Cambridge University Press:  07 September 2017

Liming Liao
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Guanghua Ji*
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Zhongwei Tang
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
Hui Zhang
Affiliation:
Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
*
*Corresponding author. Email address:ghji@bnu.edu.cn (G. Ji)
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Abstract

An adaptive finite element method is adopted to simulate the steady state coupled Schrödinger equations with a small parameter. We use damped Newton iteration to solve the nonlinear algebraic system. When the solution domain is elliptic, our numerical results with Dirichlet or Neumann boundary conditions are consistent with previous theoretical results. For the dumbbell and circular ring domains with Dirichlet boundary conditions, we obtain some new results that may be compared with future theoretical analysis.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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