| 能量依赖速度的二阶谱问题及其完全可积系 |
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| 引用本文： | 刘炜,袁书娟,王清.能量依赖速度的二阶谱问题及其完全可积系[J].石家庄铁道学院学报(社会科学版),2009(1):77-81. |
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| 作者姓名： | 刘炜 袁书娟 王清 |
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| 作者单位： | 刘炜,Liu Wei(石家庄铁道学院,数理系,河北,石家庄,050043);袁书娟,Yuan Shujuan(河北理工大学轻工学院,河北,唐山,063000);王清,Wang Qing(华北科技学院基础部,北京,101601)
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| 摘 要： | 讨论了与能量依赖速度的二阶特征值问题相联系的有限维系统的可积性,利用位势函数与特征函数之间的Bargmann约束,将Lax对非线性化,得到新的有限维Hamilton正则系统,最后借助于Ligouville意义下的完全可积系的对合解得到发展方程族的对合表示.
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| 关 键 词： | 谱问题 可积系统 对合表示 |
| 收稿时间： | 2008/11/11 0:00:00 |
The Second-order Spectral Problem with the Speed Energyand its Completely Integrable System |
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| Authors: | Liu Wei Yuan Shujuan Wang Qing |
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| Institution: | Department of Mathematics and Physics, Shijiazhuang Railway Institute;College of Light Industry , Hebei Polytechnic University;The Foundation Department, North China Institute of Science and Technology |
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| Abstract: | In this paper, the integrability which a finite dimensional Hamiltonian system is associated with a second order spectral problem with the speed energy is discussed. Moreover, according to the Bargmann constraint between the potential function and the eigenfunction , the Lax pairs are nonlinearized, Then based on the involutive solution of completely integrable Hamiltonian system in Liouville sense, the involutive solutions of the evolution equations are given. |
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| Keywords: | spectral problem integrable problem involutive representation |
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