| 一类新的2+1维非线性发展方程及其解的对合表示 |
| A New (2+1) dimensional Nonlinear Evolution Equation and the Involutive Representations of the Solutions |
| 投稿时间：2013-07-11 |
| 中文关键词:谱问题 Lax对非线性化 Bargmann系统 可积系统 对合表示 |
| 英文关键词:spectral problem ninlinearization of Lax pairs Bargmann system integrable system involutive representations |
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| 中文摘要: |
| 由线性谱问题的相容性条件得到一个新的2+1维非线性发展方程。利用位势函数与特征函数之间的约束获得Bargmann系统，通过Euler Lagrange方程及Legendre变换构造Jacobi Ostrogradsky坐标。应用Lax对非线性化方法，生成了一个新的有限维Hamilton正则系统。最后证明其为Liouville意义下完全可积系统，并得到发展方程族的对合表示。 |
| 英文摘要: |
| A new (2+1) dimensional nonlinear evolution equation is obtained based on the compatible condition of two linear spectral problems. By means of the constraint condition between the potentials and the eigenvector, the Bargmann system is generated. The Jacobi Ostrogradsky coordinate system has been found through Euler Lagrange equation and Legendre transformations. Using the nonlinearization approach of Lax pairs, a new finite dimensional Hamilton canonical equations are obtained. Finally, it is proved completely integrable systems, and the involutive solutions of the evolution equations are given. |
| 刘亚峰,刘炜.一类新的2+1维非线性发展方程及其解的对合表示[J].石家庄铁道大学学报：自然科学版,2014,(1):106-110. |
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