Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture

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Cumhuriyet Üniversitesi Fen-Edebiyat Fakültesi Fen Bilimleri Dergisi
Volume:36 Issue:3
Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture

Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture

Authors : Sm HOSEINI, H SADEGHI, S ESKANDAR

Pages : 2206-2215

View : 59 | Download : 15

Publication Date : 2015-05-13

Article Type : Review Paper

Abstract :Abstract. Using Lax representation, hereditary operator related to the Harry-Dym ( HD ) hierarchy is constructed. Also Lie analysis and Lax pair are used to drive the conserved quantities for the HD hierarchy. Lie symmetry method is also applied to study Painlev´e test for the family of HD hierarchy. It is found that for this family the Painlev´e property can be at most sufficient for integrability, but not necessary. This fact has been proved earlier for just first member of this family.
Keywords : Lie analysis, conservation laws, hereditary operator, Painlev´e property, ARS conjecture

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