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Exact Solutions of Completely Integrable Systems and Linear ODE’s Having Elliptic Function Coefficients

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Computer Algebra in Scientific Computing (CASC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4770))

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Abstract

We present an algorithm for finding closed form solutions in elliptic functions of completely integrable systems. First we solve the linear differential equations in spectral parameter of Hermite-Halphen type. The integrability condition of the pair of equations of Hermite-Halphen type gives the large family of completely integrable systems of Lax-Novikov type. This algorithm is implemented on the basis of the computer algebra system MAPLE. Many examples, such as vector nonlinear Schödinger equation, optical cascaded equations and restricted three wave system are considered. New solutions for optical cascaded equations are presented. The algorithm for linear ODE’s with elliptic functions coefficients is generalized to 2×2 matrix equations with elliptic coefficients.

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Authors and Affiliations

  1. Institute of Electronics, Bulgarian Academy of Sciences, Blvd. Tsarigradsko shosse 72, Sofia, 1784, Bulgaria

    N. A. Kostov

  2. National High School ”Sofia”, Blvd. Montevideo 21, Sofia, Bulgaria

    Z. T. Kostova

Authors
  1. N. A. Kostov
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  2. Z. T. Kostova
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Victor G. Ganzha Ernst W. Mayr Evgenii V. Vorozhtsov

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© 2007 Springer-Verlag Berlin Heidelberg

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Kostov, N.A., Kostova, Z.T. (2007). Exact Solutions of Completely Integrable Systems and Linear ODE’s Having Elliptic Function Coefficients. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2007. Lecture Notes in Computer Science, vol 4770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75187-8_20

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  • DOI: https://doi.org/10.1007/978-3-540-75187-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75186-1

  • Online ISBN: 978-3-540-75187-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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