Special polynomials associated with rational solutions of some hierarchies |
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| Authors: | Nikolai A Kudryashov |
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| Institution: | 1. School of Mathematics and Computer Science, Mianyang Normal University, Mianyang, Sichuan 621000, China;2. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, China;1. College of Sciences and Humanities Studies Al-Kharj, Physics Department, Prince Sattam Bin Abdulaziz University, Al Kharj, Saudi Arabia;2. Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Saudi Arabia;3. Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt;4. Department of Physics, Faculty of Science, Ain Shams University, Cairo, Egypt;1. Programa de Pós-Graduação em Métodos Numéricos em Engenharia, Universidade Federal do Paraná, Caixa Postal 19011, CEP 81531-980, Curitiba, PR, Brasil;2. Programa de Engenharia Civil, Universidade Federal do Rio de Janeiro, Caixa Postal 68506, CEP 21945-970, Rio de Janeiro, RJ, Brasil;1. School of Sciences, Zhejiang A&F University, Lin’an, Zhejiang 311300, PR China;2. School of Environmental & Resources, Zhejiang A&F University, Lin’an, Zhejiang 311300, PR China |
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| Abstract: | New special polynomials associated with rational solutions of the Painlevé hierarchies are introduced. The Hirota relations for these special polynomials are found. Differential-difference hierarchies to find special polynomials are presented. These formulae allow us to search special polynomials associated with the hierarchies. It is shown that rational solutions of the Caudrey–Dodd–Gibbon, the Kaup–Kupershmidt and the modified hierarchy for these ones can be obtained using new special polynomials. |
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