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Modification of the Painlevé test for systems of nonlinear partial differential equations

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Abstract

The Painlevé test in the formulation of Weiss, Tabor, and Carnevale [1] for the (2+1)-dimensional integrable model proposed by Boiti, Léon, and Pempinelli [2] is considered. It is shown that the standard procedure for truncating the series is valid only on a subset of solutions of a (1+1)-dimensional reduction of the considered problem. A modification of the series truncation procedure that allows it to be performed in the unreduced case is proposed. On this basis, a new representation of a Lax pair and also a Bäcklund transformation is obtained. It is shown that the considered system is Hamiltonian, and some special (soliton) solutions are constructed.

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Authors
  1. T. I. Garagash
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Additional information

V. A. Steklov Mathematics Institute, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No.3, pp. 367–376, August, 1994.

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Garagash, T.I. Modification of the Painlevé test for systems of nonlinear partial differential equations. Theor Math Phys 100, 1075–1081 (1994). https://doi.org/10.1007/BF01018572

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  • DOI: https://doi.org/10.1007/BF01018572

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