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

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Analysis and Partial Differential Equations: Perspectives from Developing Countries

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 275))

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad del Valle, Calle 13 Nro 100-00, Cali, Colombia

    Juan Carlos Muñoz Grajales

  2. Departamento de Ciencias Naturales y Matemáticas, Universidad Javeriana, Calle 18 no. 118-250, Cali, Colombia

    Luisa Fernanda Vargas

Authors
  1. Juan Carlos Muñoz Grajales
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  2. Luisa Fernanda Vargas
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Correspondence to Juan Carlos Muñoz Grajales .

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Editors and Affiliations

  1. School of Mathematical Sciences, Queen Mary University of London, London, UK

    Julio Delgado

  2. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium

    Michael Ruzhansky

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Muñoz Grajales, J.C., Vargas, L.F. (2019). Existence and Numerical Computation of Standing Wave Solutions for a System of Two Coupled Schrödinger Equations. In: Delgado, J., Ruzhansky, M. (eds) Analysis and Partial Differential Equations: Perspectives from Developing Countries. Springer Proceedings in Mathematics & Statistics, vol 275. Springer, Cham. https://doi.org/10.1007/978-3-030-05657-5_12

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