Existence and Numerical Computation of Standing Wave Solutions for a System of Two Coupled Schrödinger Equations

  • Juan Carlos Muñoz GrajalesEmail author
  • Luisa Fernanda Vargas
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 275)


In this paper, we consider the existence of a type of stationary wave of a system of two coupled Schrödinger equations with variable coefficients, which can be employed to describe the interaction among propagating modes in nonlinear optics and Bose-Einstein condensates (BECs), for instance. To prove existence of these solutions, we use some existing fixed point theorems for completely continuous operators defined in a cone in a Banach space. Furthermore, some numerical approximations of stationary waves are computed by using a spectral collocation technique combined with a Newton’s iteration.


Schrödinger equations Numerical computations Standing waves 



This research was supported by Colciencias and Universidad del Valle, Calle 13 No. 100-00, Cali-Colombia, under the research project 1106-712-50006.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Juan Carlos Muñoz Grajales
    • 1
    Email author
  • Luisa Fernanda Vargas
    • 2
  1. 1.Departamento de MatemáticasUniversidad del ValleCaliColombia
  2. 2.Departamento de Ciencias Naturales y MatemáticasUniversidad JaverianaCaliColombia

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