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The Painlevé property and coordinate transformations

Свойство Пенлеве и преовразование координат

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

In this paper, the question of conserving the Painlevé property of partial differential equations by coordinate transformations is studied. Also, the effects of some types of transformations of interest, like ordinary Bäcklund as well as auto-Bäcklund transformations of partial differential equations, are shown as well. Some features and comments are given.

Riassunto

In questo lavoro si studia il problema della conservazione della proprietà di Painlevé di equazioni differenziali parziali attraverso le trasformazioni delle coordinate. Si mostrano anche gli effetti di alcuni tipi di trasformazioni interessanti, come le trasformazioni ordinarie di Bäcklund nonché quelle di auto-Bäcklund di equazioni differenziali parziali. Si danno alcune caratteristiche e commenti.

Резюме

В этой статяе исследуется вопрос сохранения свойства Пенлеве для дифференциальных уравнений в частных производных с помощью преобразований координат. Также рассматриваются эффекты некоторых типов преобразований, обычного преобразования Беклунда и преобразования авто-Беклнда для дифференциаляных уравнений в частных производных. Обсуждаются некоторые особенности и резулятаты.

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Author notes

  1. M. F. El-Sabbagh & A. H. Khater

    Present address: Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah, S. Arabia

Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Minia University, Minia, Egypt

    M. F. El-Sabbagh

  2. Mathematics Department, Faculty of Science, Cairo University, Beni-Suef, Egypt

    A. H. Khater

Authors
  1. M. F. El-Sabbagh
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  2. A. H. Khater
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Traduzione a cura della Redazione.

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El-Sabbagh, M.F., Khater, A.H. The Painlevé property and coordinate transformations. Nuov Cim B 104, 123–129 (1989). https://doi.org/10.1007/BF02906310

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  • DOI: https://doi.org/10.1007/BF02906310

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