| 与广义KdV方程族相关的谱问题及其完全可积性 |
| The Spectral Problem Related to the Generalized KdV Equations and Its Completely Integrable System |
| 投稿时间：2013-01-01 |
| 中文关键词:谱问题 非线性化 Bargmann约束 可积系统 |
| 英文关键词:spectral problem ninlinearized Bargmann constraint integrable system |
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| 中文摘要: |
| 通过Lax方程获得了与二阶谱问题相联系的广义KdV方程族。利用位势函数与特征函数之间的Bargmann约束，将Lax对非线性化。由合适的Jacobi Ostrogradsky坐标，得到一个新的有限维Hamilton正则系统，并证明其是完全可积系统。最后得到发展方程族的对合表示。 |
| 英文摘要: |
| Based on the Lax equation, the generalized KdV equations hierarchy related to the 2th order eigenvalue problem is given. By the Bargmann constraint between the potentials and the eigenvector functions, the Lax pairs are ninlinearized. Using a reasonable Jacobi Ostrogradsky coordinate, a new finite dimensional Hamilton canonical equations are obtained, and proved to be completely integrable systems. Moreover, the involutive solutions of the evolution equations are given. |
| 孙海珍,刘亚峰.与广义KdV方程族相关的谱问题及其完全可积性[J].石家庄铁道大学学报(自然科学版),2013,(1):106-110. |
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