| Involutive Solutions and Commutator Representations of the Dirac Hierarchy |
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| 引用本文： | 乔志军. Involutive Solutions and Commutator Representations of the Dirac Hierarchy[J]. 数学季刊, 1997, 0(1) |
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| 作者姓名： | 乔志军 |
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| 作者单位： | Department of Mathematics，Liaoning University，Shenyang，110036 |
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| 摘 要： | ConsidertheDiracspectralproblemwherep,qaretwopotentials,Aisaspectralparameter.L*isaninjectivehomomorphism.ThefunctionalgradientVA=(2RR,ri-of)TofeigenvalueAwithrespecttop,qsatisfiesarecalledtheLenard'soperatorpairof(1).Theorem1LetG(1)(x),G(z)(x)betwoarbitarysmoothfunctions,G=(G(1),G(2))".ThenthefollowingoperatorequationwithrespecttoV=V(G),possessestheoperatorsolutionwhereL.'-jisthecommutator;L=L(p,q),K,Jaredefinedby(1)l(4)respectively.ProofSubstitute(6)into(5),directlycalculate.Defin…
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Involutive Solutions and Commutator Representations of the Dirac Hierarchy |
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| Qiao Zhijun. Involutive Solutions and Commutator Representations of the Dirac Hierarchy[J]. Chinese Quarterly Journal of Mathematics, 1997, 0(1) |
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| Authors: | Qiao Zhijun |
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| Abstract: | The Dirac hierarchy of isospectral evolution equations associated with the Dirac spectral problem are studied in this paper. The commutator representations of Dirac hierarchy are first presented, and then through the nonlinearization of Lax pair the involutive solutions of Dirac hierarchy are obtained. |
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| Keywords: | Dirac hierarchy commutator representation involutive system involutive solution |
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