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On a method for constructing algebro-geometric solutions to the zero curvature equation

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Abstract

Under special conditions that hold for a number of applications, we suggest a construction that reduces the calculation of algebro-geometric solutions of the zero curvature equation for 2 × 2 matrices to solving the Jacobi inversion problem on a hyperelliptic Riemann surface and the Riccati equation. An application to the system of equations of the principal chiral field is considered.

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Authors and Affiliations

  1. Omsk State Technical University, USA

    D. P. Novikov & R. K. Romanovskii

Authors
  1. D. P. Novikov
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  2. R. K. Romanovskii
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 61–72, January, 1997.

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Novikov, D.P., Romanovskii, R.K. On a method for constructing algebro-geometric solutions to the zero curvature equation. Theor Math Phys 110, 47–56 (1997). https://doi.org/10.1007/BF02630368

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  • DOI: https://doi.org/10.1007/BF02630368

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